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**Introduction**

One of the available techniques for predictive maintenance of rotating machines is based on vibration signal analysis. Important information about the state of a machine can be obtained by signal spectrum analysis. Vibration signal amplitudes due to bearing and gear faults are hundreds of times smaller than signal amplitudes due to often present unbalances. Generally speaking, the energy of such signals appears in frequencies which are multiple of the machine rotating frequency, and typically do not exceed 5 kHz. Thus, the spectrum must have a high resolution in frequency and large dynamic range (60 dB).

The following collector and analyzer is a portable instrument which enables an operator to collect and analyze the signal at the field. This work presents all the development steps of the instrument, from hardware, software, signal processing to performance evaluation.

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**Hardware**

Hardware design considered application specifications such as portability, reduced energy consumption and enhanced processing capability. In **Figure 1** is shown the functional block diagram of the vibration collector an analyzer. The signal of the sensor (acceleration, velocity or displacement) is amplified to guarantee a 12 bit A/D conversion. Selectable cut-off frequency (20 kHz or 10 kHz), anti-aliasing analog filters (Butterworth) matched to A/D sample frequencies (51.2 kHz or 21.6 kHz) are included. A digital signal processor (DSP) is used to implement the algorithms. Instrument operation menus and graphs of collected data are displayed on a 128 line/ 240 columns liquid crystal display. A keyboard enables the operator to choose specific functions. A serial interface enables the instrument to interchange data with PCs and compatibles. EEPROMs store routines related to signal processing, graphs and display menus. A 1 Mbyte RAM stores the signals (time and frequency domains), and data from the PC such as information about a a maintenance route (machine, positions and sensors types) and previous collected data to make comparisons possible.

**Figure 1** – Functional block diagram of the vibration collector and analyzer

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**Digital signal processing**

The conversion to the frequency domains is done by FFT (Fast Fourier Transform) algorithms. In these algorithms, for N samples in the time domain, spaced by Δt seconds are obtained N samples, called lines, equally spaced in the frequency domain between zero and the sample frequency. The distance between the spectrum lines (resolution = Δf) is given by the quotient between the sample frequency fs and the number of lines N. Thus the resolution is inversely proportional to the acquisition time T (Δf = fs/N = 1/N * Δt = 1/T).

A DIF (Decimation in Frequency) complex radix-2 FFT is used, followed by an algorithm that obtains a real 2N line FFT from a complex N line FFT (Brighman, 1974). The operator can choose the number of lines (100, 200, 400, 800, 1600, 3200) of the FFT before starting the acquisition. Considering that for real signals only half of the samples are of interest, the algorithm is efficient for a number of lines that is an integer power of two, for N lines shown, it is necessary to calculate 2.56 * N lines.

The available frequency ranges are [0 – fmax], where fmax = 20, 10, 5, 2 and 1 kHz and 500, 200, 100 and 50 Hz. A hybrid solution for the fs reduction was adopted. At first, analog filtering followed by A/D sample frequency reduction is done (**Figure 1**) and then digital filtering followed by elimination of samples, process known as decimation (**Figure 2**).

**Figure 2** – DSP processing diagram

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The cut-off frequency of the filter is set to the value of fmax, and fs is reduced to 2.56 * fmax. Thus, with fmax = 50 Hz and N = 3200, the highest resolution of the instrument, 15.5 mHz (50Hz/3200) is reached, with a real 8192 line FFT.

The main advantage of digital filters is that their characteristics do not vary with temperature and aging. Filtering process must be performed in real time. Elliptic IIR (Infinite Impulse Response) filters were developed in the direct form II approach. FIR (Finite Impulse Response) filters, if specified with the same design parameters, would yield large order filters which consume a large amount of processing time and a large memory space, failing to match other design specifications. The specifications of the pass-band and stop-band of the filters are matched to the A/D converter resolution. The fact that these filters have a non-linear phase characteristics does not matter in this case, because even if the signal is distorted in the time domain, the spectral magnitude will not be altered.

In spectrum analysis (FFT)it is necessary to convolute the input signal with a window function to minimize spectral leakage. Window functions such as *Flattop*, *Uniform* and *Hanning* (**Figure 2**) are implemented. These functions are widely used in vibration analysis.

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**Evaluation**

When implementing digital filters, window functions and FFT algorithms in finite length precision arithmetic (fixed point) some attention is needed in the following aspects (**Figure 3a**):

- Bit quantization of the A/D converter;
- Overflow;
- Coefficient quantizations (filters, window functions, “twiddle factors”);
- Finite length precision noise.

As a way to evaluating performance of the implemented algorithms, some routines were developed in MATLAB, linked with the TMS320 simulator (**Figure 3b**).

**Figure 3** – (**a**) Ideal processing x Fixed-point processing (**b**) Processing performance evaluation environment

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The strategy for evaluating the algorithms was based in comparing the results of the TMS simulator with those attained using MATLAB (floating point/ double precision). This evaluation was performed with pre-established test signals. Input signals such as an impulse, or sum of sinusoids and also white noise were applied, which as well as proving to be appropriate to the problem in question, also allowed the understanding of some process phenomena. The algorithms of FFT, filters and window functions were first evaluated separately and then altogether.

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**Conclusion**

The vibration collector/ analyzer prototype developed matched all design specifications. With this design, a knowledge in digital signal processing (DSP) applications and dedicated microprocessors was attained. The next step in evaluation will be the testing of the equipment with real machine signals, by a staff specialized in mechanical vibrations. It is important to mention that with a few modifications this device can be used on other engineering applications such as civil, electrical etc.

As a concluding remark, we emphasize that the researcher involved with the vibration analysis area must realize on the importance of DSP. Thus, some theoretical knowledge in ho the instrument works and DSP is needed.

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**Authors**

- Puhlmann, Henrique Frank W.
- Moscati, Ney R.
- Casagrande, Rogério
- Anraku, Luiz Carlos I.

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**Bibliography**

Brigham, The Fourier Transform, Prentice Hall, 1974

Burrus, C.S.;Parks, T.W., DFT/FFT and Convolution Algorithms – Theory and implementation, John Wiley & Sons, 1985

Burrus, C.S.;Parks, T.W., Digital Filter Design, John Wiley & Sons, 1987

Cooley, J.W.; Tukey, J.W., An algorithm for the Machine Computation of Complex Fourier Series, Mathematics of Computation, 19, pp. 297-301, April 1965

Oppenheim, A.V.; Schafer, R.W., Discrete-Time Signal Processing, Englewood Cliffs NJ, Prentice-Hall International, 1989

Texas Instruments, Digital Signal Processing Applications (TMS320 Family), 1986

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This work, “**Development of a portable data collector and analyzer for rotating machine vibrations**“, by Henrique Frank W. Puhlmann, Ney R Moscati, Rogério Casagrande, Luiz Carlos I. Anraku, is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.