Introduction
Among the various techniques available for predictive maintenance of rotating machines, much is used that is based on vibration signal analysis. Important information about the state of a machine can be obtained by analyzing the vibration signal spectrum. Vibration signal amplitudes due to bearing and gear failures are hundreds of times smaller than signal amplitudes due to frequent unbalance problems. Generally the energy of such signals appears at frequencies that are multiple of the machine's rotation frequency and usually do not exceed 5 kHz. Thus, the spectrum to be analyzed must have a high frequency resolution and wide dynamic range (60 dB).
The following detailed collector and analyzer is a portable instrument that allows an operator to collect and analyze the vibration signal in the field, measured directly on the machine to be analyzed. This white paper presents all stages of the development of this instrument, from hardware and software to the evaluation of signal processing performance.
Hardware
The hardware design took into account application specifications such as portability, reduced power consumption and large processing capacity. In Figure 1 is shown a functional block diagram collector and vibration analyzer. The sensor signal (acceleration, velocity or displacement) is amplified to ensure a 12-bit A / D conversion with maximum use of its dynamic range. Selectable cut-off frequencies (20 kHz or 10 kHz) and Butterworth-type analog anti-aliasing filters matching the A / D converter sampling frequencies (51.2 kHz or 21.6 kHz) were also considered. A fixed point digital signal processor (DSP) was used to implement the necessary algorithms.
Instrument operation menus and graphs of collected data are displayed on a graphical liquid crystal display that has 128 rows x 240 columns. A keyboard allows the operator to choose specific functions by navigating through the menus. A serial interface allows the instrument to exchange data with PCs and compatible devices. EEPROMs store program routines related to graphics, signal processing and menu display. A 1 MByte RAM memory stores field-collected signals (time and frequency domains) and PC data, such as information about a particular maintenance route (machine types, sensors and the positions to fix them) and previously collected data to enable comparisons.
Digital signal processing
The conversion to frequency domains is done by applying Fast Fourier Transform ( FFT) algorithms . Through these algorithms, for N time domain samples spaced by Δt seconds, N samples are obtained, called lines or rays, equally spaced in the frequency domain in the range between zero and the sampling frequency. The distance between the spectrum lines (resolution = Δf) is given by the quotient between the sampling frequency (fs) and the number of N lines. Thus, the resolution is inversely proportional to the total acquisition time T (Δf = fs / N = 1 / N * Δt = 1 / T).
For the calculation of spectrum lines, a complex DIF (frequency decimation) type base-2 FFT is used, followed by an algorithm that obtains 2N real number lines from the calculation of a complex N-line FFT (Brighman , 1974) in order to achieve more speed and efficiency in calculations. From the menus, the operator can choose the number of lines (100, 200, 400, 800, 1600, 3200) of the FFT before starting acquisition. Since the measured signals are real (not complex) and in this case only half of the samples are of interest, the algorithm is most efficient for a number of lines that are an integer power of two. Thus, for N lines shown, it is necessary to calculate 2.56 * N lines.
The frequency ranges available in the equipment are [0 - fmax], where fmax = 20, 10, 5, 2 and 1 kHz and 500, 200, 100 and 50 Hz. A hybrid solution for fs reduction has been adopted. In the beginning an analog filtering is performed, followed by an A / D conversion, where a reduction of the sampling frequency is made ( Figure 1 ). Then the signal goes through a digital filtering followed by a sampling, a process known as decimation
The digital filter cutoff frequency is internally set to the value of fmax, and the signal sequence sampling frequency is reduced to 2.56 * fmax. Thus, for example, at fmax = 50 Hz and N = 3200 the highest resolution of the instrument is reached: 15.5 mHz (50Hz / 3200) by means of a real 8192 line FFT.
The main advantage of using digital filters is that their characteristics do not vary with temperature or aging. For this equipment, the filtration process must be performed in real time. For this purpose, Infinite Impulse Response (IIR) type elliptical digital filters were developed using the direct form II approach. If Fite ( Finite Impulse Response) type filters were specified) with the same design parameters would generate very high order filters that would consume a large amount of processing time and a large amount of memory. It would not be possible to meet other design specifications if FIR filters were used. Filter passband and rejection band specifications are compatible with A / D converter resolution. The fact that IIR filters have the characteristic of distorting the signal phases nonlinearly is not important in this case, because even if the signal is distorted in the time domain, the spectral magnitude does not change.
Spectrum analysis (FFT) also requires convolution of the input signal with a windowing function to minimize unwanted spectral leakage . For this, windowing functions such as Flattop, uniform and Hanning were also implemented. These functions are widely used in vibration analysis.
Evaluation
When implementing digital filters, windowing functions, and FFT algorithms in finite length (fixed point) precision arithmetic, a little more attention needs to be paid to the following aspects, which may affect equipment accuracy and performance. :
Bit quantization of A / D converter;
Overflow of the calculated value;
Quantization of coefficients (filters, windowing functions, FFT twiddle factors );
Noise due to finite length precision.
As a way to evaluate the performance of the implemented algorithms, some MATLAB routines have been developed, linked with the TMS320 simulator for the Texas Instruments TMS320C2x DSP family.
The strategy for evaluating the algorithms was based on comparing the results of the DSP simulator with those obtained using the double precision floating point (MATLAB). This evaluation was performed with previously established test signals. Input signals such as a unit pulse or the sum of sine waves of various frequencies as well as white noise were applied to the equipment. These signals proved to be appropriate as test stimuli as well as some phenomena of the process. The FFT algorithms, filtering and windowing functions were initially evaluated separately and then together.
Conclusion
The prototype of the developed collector and vibration analyzer met all design specifications. This project has achieved a good level of knowledge in digital signal processing (DSP) applications and dedicated microprocessors.
Among the various techniques available for predictive maintenance of rotating machines, much is used that is based on vibration signal analysis. Important information about the state of a machine can be obtained by analyzing the vibration signal spectrum. Vibration signal amplitudes due to bearing and gear failures are hundreds of times smaller than signal amplitudes due to frequent unbalance problems. Generally the energy of such signals appears at frequencies that are multiple of the machine's rotation frequency and usually do not exceed 5 kHz. Thus, the spectrum to be analyzed must have a high frequency resolution and wide dynamic range (60 dB).
The following detailed collector and analyzer is a portable instrument that allows an operator to collect and analyze the vibration signal in the field, measured directly on the machine to be analyzed. This white paper presents all stages of the development of this instrument, from hardware and software to the evaluation of signal processing performance.
Hardware
The hardware design took into account application specifications such as portability, reduced power consumption and large processing capacity. In Figure 1 is shown a functional block diagram collector and vibration analyzer. The sensor signal (acceleration, velocity or displacement) is amplified to ensure a 12-bit A / D conversion with maximum use of its dynamic range. Selectable cut-off frequencies (20 kHz or 10 kHz) and Butterworth-type analog anti-aliasing filters matching the A / D converter sampling frequencies (51.2 kHz or 21.6 kHz) were also considered. A fixed point digital signal processor (DSP) was used to implement the necessary algorithms.
Instrument operation menus and graphs of collected data are displayed on a graphical liquid crystal display that has 128 rows x 240 columns. A keyboard allows the operator to choose specific functions by navigating through the menus. A serial interface allows the instrument to exchange data with PCs and compatible devices. EEPROMs store program routines related to graphics, signal processing and menu display. A 1 MByte RAM memory stores field-collected signals (time and frequency domains) and PC data, such as information about a particular maintenance route (machine types, sensors and the positions to fix them) and previously collected data to enable comparisons.
Digital signal processing
The conversion to frequency domains is done by applying Fast Fourier Transform ( FFT) algorithms . Through these algorithms, for N time domain samples spaced by Δt seconds, N samples are obtained, called lines or rays, equally spaced in the frequency domain in the range between zero and the sampling frequency. The distance between the spectrum lines (resolution = Δf) is given by the quotient between the sampling frequency (fs) and the number of N lines. Thus, the resolution is inversely proportional to the total acquisition time T (Δf = fs / N = 1 / N * Δt = 1 / T).
For the calculation of spectrum lines, a complex DIF (frequency decimation) type base-2 FFT is used, followed by an algorithm that obtains 2N real number lines from the calculation of a complex N-line FFT (Brighman , 1974) in order to achieve more speed and efficiency in calculations. From the menus, the operator can choose the number of lines (100, 200, 400, 800, 1600, 3200) of the FFT before starting acquisition. Since the measured signals are real (not complex) and in this case only half of the samples are of interest, the algorithm is most efficient for a number of lines that are an integer power of two. Thus, for N lines shown, it is necessary to calculate 2.56 * N lines.
The frequency ranges available in the equipment are [0 - fmax], where fmax = 20, 10, 5, 2 and 1 kHz and 500, 200, 100 and 50 Hz. A hybrid solution for fs reduction has been adopted. In the beginning an analog filtering is performed, followed by an A / D conversion, where a reduction of the sampling frequency is made ( Figure 1 ). Then the signal goes through a digital filtering followed by a sampling, a process known as decimation
The digital filter cutoff frequency is internally set to the value of fmax, and the signal sequence sampling frequency is reduced to 2.56 * fmax. Thus, for example, at fmax = 50 Hz and N = 3200 the highest resolution of the instrument is reached: 15.5 mHz (50Hz / 3200) by means of a real 8192 line FFT.
The main advantage of using digital filters is that their characteristics do not vary with temperature or aging. For this equipment, the filtration process must be performed in real time. For this purpose, Infinite Impulse Response (IIR) type elliptical digital filters were developed using the direct form II approach. If Fite ( Finite Impulse Response) type filters were specified) with the same design parameters would generate very high order filters that would consume a large amount of processing time and a large amount of memory. It would not be possible to meet other design specifications if FIR filters were used. Filter passband and rejection band specifications are compatible with A / D converter resolution. The fact that IIR filters have the characteristic of distorting the signal phases nonlinearly is not important in this case, because even if the signal is distorted in the time domain, the spectral magnitude does not change.
Spectrum analysis (FFT) also requires convolution of the input signal with a windowing function to minimize unwanted spectral leakage . For this, windowing functions such as Flattop, uniform and Hanning were also implemented. These functions are widely used in vibration analysis.
Evaluation
When implementing digital filters, windowing functions, and FFT algorithms in finite length (fixed point) precision arithmetic, a little more attention needs to be paid to the following aspects, which may affect equipment accuracy and performance. :
Bit quantization of A / D converter;
Overflow of the calculated value;
Quantization of coefficients (filters, windowing functions, FFT twiddle factors );
Noise due to finite length precision.
As a way to evaluate the performance of the implemented algorithms, some MATLAB routines have been developed, linked with the TMS320 simulator for the Texas Instruments TMS320C2x DSP family.
The strategy for evaluating the algorithms was based on comparing the results of the DSP simulator with those obtained using the double precision floating point (MATLAB). This evaluation was performed with previously established test signals. Input signals such as a unit pulse or the sum of sine waves of various frequencies as well as white noise were applied to the equipment. These signals proved to be appropriate as test stimuli as well as some phenomena of the process. The FFT algorithms, filtering and windowing functions were initially evaluated separately and then together.
Conclusion
The prototype of the developed collector and vibration analyzer met all design specifications. This project has achieved a good level of knowledge in digital signal processing (DSP) applications and dedicated microprocessors.
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