Journal of the Balkan Tribological Association Vol. 26, No 2, 367–382 (2020) Technological tribological processes AN INVESTIGATION ON SOUND ANALYZER EFFECTS IN WHIRLING OF SHAFT APPARATUS N. NAVANEETHAKANNAN*, P. SIVANANDI, V. M. NATARAJAN, M. THANIGACHALAM Government College of Technology, Coimbatore, Tamil Nadu, India E-mail: nnanthu@yahoo.com,sivaperiyyasamy@gmail.com, vivekmasthiraj@rediffmail.com, mugilanapec@gmail.com ABSTRACT Signal processing technology represents a new technique for analysing sounds in mechanical structures. The sound analyser converts an information into signals for making the process effective. Current research has focussed on comparing the performance of sound analyser with accelerometer for analysing the rotating machinery, which integrates norm of residuals and damping ratio through power spectral density behaviour to enhance an accuracy of predicting the vibration. The aim of this investigation is to determine a method to extract vibrational features with increased performance. Sound analyser technology is to be processed by using MATLAB in this project. Keywords: signal processing, accelerometer, norm of residuals, power spectral density, damping ratio, MATLAB. AIMS AND BACKGROUND Vibrational analysis is the major criteria when considering rotating shafts. Whirling is defined as the rotation of the plane made by the line of centres of the bearings and the bent shafts. As the shaft rotates in any machine tools, vibration also will exist due to an eccentricity. It causes more defects for the machine tools when an exciting frequency meets the natural frequency. So, prediction of vibration in machine tools is mandatory. Moreover, an accuracy of prediction also depends upon the selection of analysing process. * For correspondence. 367 EXPERIMENTAL WORK Whirling of shaft specifications Diameter of the shaft Length of the shaft Young’s modulus of the material Density of the steel Mass of the shaft, (M) = 0.005 m = 1.02 m = 2.06*1010 N/m2 = 7850 kg/m3 = (π/4)*d2 *l*ρ = (π/4)*0.52 *102*7850*10-6 = 0.1571 kg Mass per unit of length = 0.1571/102 = 1.54*10-1 kg/m Critical speed of the shaft (Mode I) = 1400 RPM (based on observation) Experimental calculations. The required experimental study has been performed on the whirling of shaft apparatus and an investigation done through MATLAB. It includes two types of analysis such as: Contact Analysis and Contactless Analysis Norm of residuals. The norm of residuals is a measure of the deviation between correlation and the data. A lower norm signifies a better fit. Contact Analysis – Accelerometer. The selected speeds are 850, 950, 1150, 1350 RPM. Accelerometers are available that can measure acceleration in one, two, or three orthogonal axes. Through accelerometer the variation of vibrational energy is to be measured by signal analysis. The respective signal for various speeds is shown below: Fig. 1. Effect of norm of residuals on contact analysis: power spectral density at 850 RPM 368 Fig. 2. Effect of Norm of residuals on contact analysis: power spectral density at 950 RPM Fig. 3. Effect of norm of residuals on contact analysis: power spectral density at 1150 rpm 369 Fig. 4. Effect of norm of residuals on contact analysis: power spectral density at 1350 rpm The signal 1 shows the energy intensity of vibration while rotating. It is observed that the variation of power spectrum magnitude is reducing and making the higher degree polynomials with the norm of residuals of 51.1872. The signal 2 continuously varies with respect to time, it is considered as random nature. It is observed that the variation of power spectrum magnitude is considerably lower than the previous speed. The signal 3 started to show its nature to be sinusoidal when it closes to mode 1, due to the severity of oscillations. It is observed that the variation of power spectrum magnitude is considerably lower and it signifies that it contains more vibrational energy. The maximum energy in Fig. 3 is observed when the system initiates. A lesser norm of residuals signifies higher oscillations in the system. The signal 4 follows the sinusoidal motion and it attains the maximal severity, due to its approximately reaching the mode 1. It is observed that the variation of the power spectrum magnitude as 42.9701, it causes more damage than the previous three speeds. The maximum of vibrational energy in Fig. 4 is observed when it reaches closer to mode 1. Contactless Analysis – Sound Analyser. Sound analyser quality metrics cover a wide range of parameters such as gain, noise, harmonic and frequency response. This process required to receive stimulus signals for the known characteristics. Sound analyser finds use for analyzing the signals more effectively than any other. This type of method is considered as contactless process. 370 Fig. 5. Effect of norm of residuals on contactless analysis: power spectral density at 850 rpm Fig. 6. Effect of norm of residuals on contactless analysis: power spectral density at 950 rpm 371 Fig. 7. Norm of residuals effect of on contactless analysis: power spectral density at 1150 rpm Fig. 8. Effect of Norm of residuals on contactless analysis: power spectral density at 1350 rpm The signal 5 shows the energy intensity of vibration while rotating and it is observed through a sound analyser pro. It follows an undamped oscillation criterion, which makes the system, vibrational energy decays continuously with respect to frequency. In Fig. 5 the spectral variation of norm of residuals is 24.6686. The signal 6 reveals the nature of the problem. The component is vibrating with the power spectrum magnitude of 23.961, which shows that the energy is reducing continuously with respect to frequency. A spectrum shows the frequencies, at which vibration occurs; it is a very useful analytical tool. The signal 7 shows that the power spectrum magnitude is 21.5813, which reveals that the vibrational ener372 gy variation is considerably more than other. A spectrum displays vital information that is hard to extract from a waveform. The system vibrates with enormous oscillations due to being closer to critical speed. And the decaying of vibrational energy takes more time period. The signal 8 shows that the reduction of variation is 12.9369. Comparison of Contact and Contactless Analysis  It can be observed from the Table 1, that the prediction of oscillations through sound analyser are far more than by the Accelerometer.  Based on the observation from Table 1 that 1350 RPM should have more variation than any other, because when the shaft rotates nearer to the critical speed, then the Accelerometer (Contact) shouldn’t behaves properly and also sensors getting damaged.  Due to rigorous oscillations the possibilities of measurements should only be observed by sound analyser (Contactless). Table 1. Comparison of ornm of residuals at various speeds S. No 01 02 03 04 Speed (RPM) 850 950 1150 1350 Norm of residuals (Contact) 51.18 43.84 42.98 42.97 Norm of residuals (Contactless) 24.66 23.96 21.58 12.93 Percentage variation (%) 51.81 45.34 49.79 69.90 Percentage Variation (%) Norm of Residuals 100 90 80 70 60 50 40 30 20 10 0 850 950 1150 Speed 1350 Contact Contactless Fig. 9. Percentage of variation of norm of residuals Damping Ratio. Within an oscillatory system that has the effect of reducing, it is restricting its oscillations. In machine tools, damping is produced by the process that dissipates the energy stored in an oscillation. There are three possibilities of damping which are in real life: • Over Damped System • Critical Damped System 373 • Under Damped System The oscillatory system needs to calculate damping ratio, because it makes use of how rapidly the oscillations decay from one bounce to the next. The damping ratio shows that the machine tools are vibrating at any one of the above particular damping. The damping ratio for frequency domain are expressed as: 1 Z= Q 2 Q= Res ( f ) H ( f ) − L( f ) where, Z – Damping Ratio; Q – Frequency ratio; Res (f) – Resonance frequency; H (f) – High frequency; L (f) – Low frequency. Contact Analysis – Accelerometer. The signal 10 shows the amplitude as well as reduction of variation in oscillation. It varies randomly with respect to frequency. It is observed that the variation of power spectral density is considerably reducing from 31 to 10 dB/rad/sample. The signal 11 continuously varies with respect to time, it is considered as random nature. It is observed that the variation of power spectral density considerably reducing from 32 to 10 dB/rad/sample, the respective variation is received as like as 850 RPM. The signal 12 started to show its Fig. 10. Effect of damping ratio on contact analysis: power spectral density at 850 RPM 374 Fig. 11. Effect of damping ratio on contact analysis: power spectral density at 950 RPM Fig. 12. Effect of damping ratio on contact analysis: power spectral density at 1150 RPM 375 Fig. 13. Effect of damping ratio on contact analysis: power spectral density at 1350 RPM nature to be sinusoidal when it closes to mode 1, due to severity of oscillations. It is observed that the variation of power spectral density is considerably reducing from 35 to 11 dB/rad/sample. The maximum of vibrational energy in Fig. 12 is observed when the system initiates. The signal 13 follows the sinusoidal motion and it attains the maximal severity, due to it approximately reaches the mode 1. It is observed that the variation of power spectral density is considerably reducing from 35 to 10 dB/rad/sample. The maximum of vibrational energy in Fig. 13 is observed when it reaches closer to mode 1. Contactless Analysis – Sound Analyser. In this contactless analysis, the wave pattern follows the linear phenomenon, which is repeated continuously. This analysis is to be carried out for the selected pattern from the time period of 0 to 0.00456sec., the required calculations are shown in Appendix A. The Figs 14, 15, 16 and 17 show the reduction of decaying of vibrational energy, when speed increases. It follows an undamped oscillation criterion, which makes the system, vibrational energy decays continuously with respect to frequency. In Fig. 14 the spectral variation is –21 dB to –33 dB and the damping ratio is shown in appendix A. The signal 15 reveals the nature of the problem. The component is vibrating with the power spectrum magnitude of –16 dB to –29 dB, which shows that the energy is reducing continuously with respect to frequency. A spectrum shows the frequencies, at which vibration occurs; it is a very 376 Fig. 14. Effect of damping ratio on contactless analysis: power spectral density at 850 rpm Fig. 15. Effect of damping ratio on contactless analysis: power spectral density at 950 RPM 377 Fig. 16. Effect of damping ratio on contactless analysis: power spectral density at 1150 rpm Fig. 17. Effect of damping ratio on contactless analysis: power spectral density at 1350 rpm useful analytical tool. The signal 16 shows that the power spectrum magnitude is –16 dB to –31 dB, which reveals that the vibrational energy variation is considerably more than other. A spectrum displays vital information that is hard to extract from a waveform. The system vibrates with enormous oscillations due to its being closer to critical speed. And the decaying of vibrational energy takes more time period. The signal 17 shows that the reduction of variation is –46 dB from –10 dB. 378 Comparison of Contact and Contactless Analysis • Based on an observation from the Fig. 3, the damping ratio of accelerometer takes very rapidly moves from one bounce to the next than the damping ratio of Sound analyser. Table 2. Comparison of Damping Ratio at various speeds S. No 01 02 03 04 Speed (RPM) 850 950 1150 1350 Damping Ratio (Contact) 0.55 0.52 0.48 0.46 Damping Ratio (Contactless) 0.96 0.88 0.76 0.32 Percentage Variation (%) 74.54 69.23 58.33 30.43 Percentage Variation (%) Damping Ratio 100 90 80 70 60 50 40 30 20 10 0 850 950 1150 Speed 1350 Contact Contactless Fig.18. Percentage variation of damping ratio • In general, the damping ratio at critical speed should be close to zero (reference). In that case, the calculated damping ratio of 1350 RPM by sound analyser contains 0.32, which is comparably closer to zero than that by accelerometer, which contains 0.42. • It shows that the measurements of contactless analysis are closer to zero and also whenever the rotating shaft exciting speed is closer to critical speed, the system excites enormous oscillations (reference), the damping ratio should be close to zero (reference). CONCLUSIONS This paper proposes an approach using sound analyser to extract vibrational features caused by faults in rotating machinery. This approach detects Fourier coefficients and linear phenomenon of vibrational features are to be shown, based on an observation. • Both Accelerometer and Sound Analyser measurements were analysed. From the comparison, it was seen that the prediction of vibrational features are more for sound analyser than those for the accelerometer. 379 • From the norm of residual calculations, it is shown that vibrational features of sound analyser are as follows:  51.81% more than an Accelerometer for 850 RPM.  45.34% more than an Accelerometer for 950 RPM.  49.79% more than an Accelerometer for 1150 RPM.  69.90% more than an Accelerometer for 1350 RPM. • From the damping ratio calculations, it shows that vibrational features of sound analyser are  74.54% more than an Accelerometer for 850 RPM.  69.23% more than an Accelerometer for 950 RPM.  58.33% more than an Accelerometer for 1150 RPM.  30.43% more than an Accelerometer for 1350 RPM. • For 1350 RPM, both norm of residuals and damping ratio indicate notable differences than other speeds, due to its being closer to critical speed. • The results demonstrate that the notable effectiveness of the proposed approach in extracting the vibrational features for predicting faults in rotating machinery. 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Appendix B Real Fourier series: ∞ nπx nπx   x(t ) = a0 / 2 + ∑  an cos + bn sin  L L  n =1  Fourier coefficients: T /2 an = 2 x(t )cos n ωt dt T −T∫/ 2 bn = 2 x(t )sin n ωt dt T −T∫/ 2 T /2 Euler’s formula: eiq = cos q + i sin q e − iq = cos q − i sin q ∞  einωt + e − inωt einωt − e − inωt  x(t ) = a0 / 2 + ∑  an + bn  2 2i n =1   x(t ) = ∞ ∑ (c e n =−∞ inωt n ) an − ibn 2 an + ibn C− n = 2 a0 C0 = 2 Cn = Between the real and complex Fourier coefficients, the certain relationship formed as: T /2 Cn = 1 x(t )e − inωt dt T −T∫/ 2 n = 0, ± 1, ± 2... ... 381 The matrix should be equal on both sides like symmetry about n= 0 and skew symmetry about n=0. Cn = Cne –iqn When the absolute value Cn = 382 an2 + bn2 2 − amplitude spectrum