MODELING AND CHARECTERIZATION OF CRACK DEPTH ON ROTOR BEARING USING ARTIFICIAL NEURAL NETWORKS

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 3, March 2018, pp , Article ID: IJMET_09_03_083 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed MODELING AND CHARECTERIZATION OF CRACK DEPTH ON ROTOR BEARING USING ARTIFICIAL NEURAL NETWORKS V Sudheer Kumar Assistant Professor, Department of Mechanical Engineering, V R Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India Dr. CH Nagaraju Professor, Department of Mechanical Engineering, V R Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India Dr. K Venkatrao Professor, Department of Mechanical Engineering, Vignan Foundation for Science Technology and Research University, Vadlamudi, Andhra Pradesh, India ABSTRACT Vibration in rotating machinery is caused by imbalance, misalignment, mechanical looseness, shaft crack, and other malfunctions. The diagnostics of rotor faults have been gaining importance in recent years. In the present study, vibration characteristics of cracked steel shaft were studied. A 25mm diameter and 400 mm length of steel shaft is supported on two bearings at both ends and a 1.2 kg mass of disc is held at the centre of shaft was Studied. Experiments were conducted on cracked steel shaft at different speeds and depth of cracks. Experimental results of amplitude of vibration and frequency were measured at two bearings using an accelerometer in axial, horizontal and vertical directions. Interaction effect of speed and crack depth on the responses was studied using response surface methodology. Predictive models for the responses were developed using Artificial Neural Networks (ANN). The ANN models were training with feed forward back propagation algorithm and the network was used to predict frequency and amplitude of bearing vibration. The predicted values were compared with the collected experimental data and percentage error was computed. The results show that the trained ANN models have better performance to identify the crack location and depth with higher accuracy and efficiency. Further, it can be used in fast identification of crack fault in rotating machinery. Keywords: ANN, vibration analysis, FFT Analyser, crack detection, Crack propagation editor@iaeme.com

2 Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks Cite this Article: V Sudheer Kumar, Dr. CH Nagaraju and Dr. K Venkatrao, Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks, International Journal of Mechanical Engineering and Technology, 9(3), 2018, pp INTRODUCTION Increasing demand for higher speeds and loads, led to highly flexible rotors and this makes the study of the vibratory motion essential to design. The dynamics and diagnostics of a cracked rotor have been gaining importance in recent years. The early detection of faults like fatigue cracks in rotor shafts are very important to prevent catastrophic failure of the rotor system. Vibration monitoring during start up or/and shut-down is an important task in steady state operation to detect cracks especially for machines such as aircraft engines which start and stop quite frequently and run at high speeds. Detection, location and analysis of faults play a vital role in the field of rotor dynamics. Appearances and expansion of fatigue crack in large rotating machines may lead to catastrophic failures. Online detection of cracks is very important for engineers who are working in the areas of machine dynamics. The research in the past few decades on cracked structures and rotors is well described by Wauer [1]. In extraction of hidden features from the crack, the time signal obtained from the transient analysis has to be processed or transformed to different domains like FFT, wavelet transform, etc. Depending on the characteristics of the signal like linear or non- linear, stationary or nonstationary the signal processing technique has to be selected [2]. The vibration components that are affected by crack will also be affected by misalignment and the fault diagnosis using vibration signature is essential to avoid catastrophic failure of the machine, in case of either crack or misalignment [3]. Recent studies have made investigations on misalignment, improper machine assembly and thermal distortion of the bearing housing and analyzed the resulting abnormal rotating pre-load and the effects of coupling misalignment on the vibration of the connected rotor systems [4-8]. Determination of rotor dynamic characteristics such as critical speeds, imbalance response and stability become important for design of these rotors. Typical industrial rotor is imbalanced and may carry elements such as bladed discs, impellers and is supported by bearings. Development of improved mathematical models and solution procedures for accurate and reliable prediction of behavior of these complex systems have received wide spread attention [9]. Jeffcott [10] has done one of the earliest studies on prediction of critical speeds. In his study, the rotor was modeled as a single mass mounted symmetrically on a shaft supported on two identical bearings at the ends. Prohl, [11] calculated the bending critical speeds of a general lumped parameter flexible rotor system. Then it was possible to calculate higher critical speeds, which was not possible with earlier methods as they gave only the fundamental natural frequency. With the matrix interaction procedure proposed by Thomson [12], Pestel and Lekie, [13], it was made possible to find critical speeds and associated mode shapes. Undamped critical speed calculation is not a realistic attempt to predict the actual dynamic behavior of rotor systems. The response of the rotor depends on the extent and distribution of imbalance in the rotor. The most important excitation in rotor systems is the one due to residual imbalance and different factors influencing it. Asymmetrical shafts carrying a disc of asymmetrical stiffness supported on flexible bearings are investigated by Yamamoto and Ota, [14]. Extensive experimental study of imbalance response under a variety of conditions concerning flexible shafts with discs having different inertia properties, bearing flexibilities and structural hysteresis was conducted by Downham [15] editor@iaeme.com

3 V Sudheer Kumar, Dr. CH Nagaraju and Dr. K Venkatrao The development of damage identification techniques for vibrating structures such as turbines, generators, motors, aircraft structures and large space structures has recently become a focus of substantially growing research efforts [16]. Many researchers have realized that the importance of the cracked structures, in particular the dynamics of cracked rotors, which is well documented in a book by Dimarogonas and Paipetis, [17], followed by a literature survey by Wauer, [18], more recently a survey on simple rotors by Gasch, [19] and general cracked Structures by Dimarogonas, [20]. Critical review and survey on dynamics of cracked rotors are done in the present study through the following topics (i) modeling (ii) crack detection techniques (iii) condition monitoring techniques (iv) sensitivity studies. This review includes modeling and detection of cracked structures also, since these are very relevant to cracked rotors. Finite element method (FEM) is one of the techniques often used for the modeling of cracked rotors. A special beam finite element was derived for the region of the crack by Schmied and Kramer, [21]. The opening and closing of the crack was regulated by a sinusoidal function of frequency and is equal to the frequency of rotation. Using a similar approach Bachschmid et al. [22] had substituted the cracked area with an equivalent beam finite element. An explicit formulation of another cracked element was given by Nelson and Nataraj, [23]. They used FEM in complex coordinate form to formulate the system equation of motion. A general approach to the dynamics of cracked shafts for describing crack breathing using finite element methods was developed by Li et al. [24]. The modeling of breathing cracks was simplified to switching crack by Lee et al. [25]. In case of switching crack, the cross coupled stiffness are neglected and direct stiffness have bi- levels, which are the functions of the sign of the response in the ζ-direction. The validity of the switching crack model and crack opening/closing conditions was proved through numerical simulations and experiments, and a crack identification scheme based on the analysis was also proposed. Based on the above literature, it was observed that measurement and analysis of the vibration of rotating machinery make it possible to detect and locate important faults such as mass imbalance, bearing faults, coupling misalignment and cracked shafts. A detailed study of the vibration behavior of cracked rotating shafts is an important problem area for engineers working in the field of dynamics of machines. In the present paper, vibration characteristics of cracked shaft, a steel shaft with disk mounted at its center and supported by two bearings was studied. A neural network models for amplitude and frequency of bearing vibration were developed and trained with experimental data. The models were used to predict the responses. 2. EXPERIMENTAL PROCEDURE An Experimental set up is prepared to conduct afore mentioned as shown in the Fig. 1, 25mm diameter and 400 mm length of steel shaft is supported on two bearings at both ends and a 1.2 kg mass of disc is held at the centre of shaft. A crack with depth of 1mm is made on the shaft at a distance of 256mm from one end and experiments have been conducted at different shaft speeds of 300, 500, 750, 1000, 1200 and 1500 rpm. An accelerometer is held at one of the bearing to measure vibration of shaft in the form of acoustic emission (AE) signals. The vibration signals are collected in three directions like axial, horizontal and vertical directions. The same procedure is repeated for crack depths of 2mm, 3mm, 4mm, 5mm and 6mm. A Fast Fourier transform is used to process the signal in to frequency domain. The collected data from the FFT analyzer is again transferred to the computer to generate the wave forms. Amplitude spectrums at crack depth of 1mm and shaft speed of 1000rpm for bearing 1 and 2 in horizontal direction are shown in the Fig. 2 and 3 respectively editor@iaeme.com

4 Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks Figure 1 Experimental set up of rotor kit with FFT analyzer Figure 2 Amplitude spectrum for 1000rpm for bearing 1 crack depth 1mm Horizontal Position Figure 3 Amplitude spectrum for 1000rpm for bearing 2 crack depth 1mm Horizontal Position 3. RESULTS AND DISCUSSION 3.1. ANALYSES OF EXPERIMENTAL DATA FOR BEARING1 The experimental results of amplitude and frequency of shaft vibration in axial, horizontal and vertical directions at bearing 1 are presented in the Table 1, and the interaction effect of shaft speed and crack depth on amplitude and frequency of shaft vibration has shown in Figures 4 & editor@iaeme.com

5 V Sudheer Kumar, Dr. CH Nagaraju and Dr. K Venkatrao Table 1 Amplitude and frequency values of bearing 1 S. No. Depth Speed Aa Ah Av Fa Fh Fv editor@iaeme.com

6 Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks Figure 4 Interaction effect of shaft speed and crack depth on amplitude of shaft vibration Figure 5 Interaction effect of shaft speed and crack depth on frequency of shaft vibration Interaction effect of shaft speed and crack depth on amplitude of shaft vibration in the axial, horizontal and vertical directions was presented in the Fig. 4. From the Fig. 4 (a), the amplitude of shaft vibration was observed to be high at shaft speed of 500rpm and crack depth of 2mm. The irregular correlation among amplitude, crack depth and shaft speed was also observed. In Fig 4(b) it was observed that the amplitude is high at all crack depths (1mm to 6mm) at shaft speed 1500rpm. Similarly, at Fig 4(c) it was observed that the amplitude is rising gradually with Shaft speed and Crack Depth. Interaction effect of shaft speed and crack depth on frequency of shaft vibration in the axial, horizontal and vertical directions is presented in the Fig. 5. From the Fig. 5(a), the frequency of shaft vibration was observed to be high at shaft speed 1000 rpm and crack depth of 4mm. It was also observed that a sudden rise correlation among frequency due to crack depth 1mm to 6mm and shaft speed 300rpm to 1500rpm. As shown in Figure 5(b), the frequency in Y Direction (Fy) was found to be high at shaft speeds of 1000 rpm and 1500 rpm for three depths of cracks. But, the frequency at Z Direction is high at crack depth of 2mm for shaft speed of 500rpm. As the Load applied in Y Direction, the frequency was found to be high in Y Direction at shaft speeds of 1000 rpm and 1500 rpm. The frequency of vibration in X Direction (Fy) was shown in the Figure 5(c), the Fx was found to be high at a combination of crack depth 6mm and shaft speed 500 rpm. At shaft speed of 1000 rpm and 1500 rpm, the Fx is not high at all the crack depths Analyses of experimental data for bearing 2 The experimental results of amplitude and frequency of shaft vibration in axial, horizontal and vertical directions at bearing 2 are presented in the Table 2, and the interaction effect of shaft speed and crack depth on amplitude and frequency of shaft vibration has shown in Figures 6 and editor@iaeme.com

7 V Sudheer Kumar, Dr. CH Nagaraju and Dr. K Venkatrao Table 2 Amplitude and Frequency Values of Bearing 2 Sample No Depth Speed Aa Ah Av Fa Fh Fv editor@iaeme.com

8 Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks Figure 6 Interaction effect of crack depth and speed on amplitude of shaft vibration Figure 7 Interaction effect of crack depth and speed on frequency of shaft vibration Interaction effect of shaft speed and crack depth on amplitude of shaft vibration in the axial, horizontal and vertical directions is presented in the Fig. 6. From the Fig. 6 (a), (b) and (c) it was observed that amplitude is rising gradually with speed and depth of crack. Interaction effect of shaft speed and crack depth on frequency of shaft vibration in the axial, horizontal and vertical directions is presented in the Fig 7. from the Fig 7(a), the frequency of shaft vibration was observed to be high at 1000rpm of shaft speed. The irregular correlation among frequency, crack depth and shaft speed was also observed at Fig 7(b). Similarly, at 7(c) it was observed that frequency is high at 4mm and 6mm depth. 4. ARTIFICIAL NEURAL NETWORKS An artificial neural network (ANN) is used in many applications as data processing system that consists of large number of processing elements in an architecture influenced by cerebral cortex portion of the brain. The ANN is used to develop prediction models in order to develop relationship between dependent (responses) and independent variables. These models are being successfully used to predict responses and also used to optimize process parameters. The ANNs are also called as neuromorphic systems, models and parallel distributed processing models. The ANN structure is constructed with dense interconnection of simple computational elements and these elements are operated in parallel to get high performance speed [26] editor@iaeme.com

9 V Sudheer Kumar, Dr. CH Nagaraju and Dr. K Venkatrao Figure 8 Neural Network Architecture ( ) In the present work, a four layered ( ) network models were constructed for the two bearings as shown in the Fig.8. The first layer is input layer which has two neurons named as speed and depth of crack, fourth layer is output layer that has six neurons named as amplitude and Frequency of vibration in axial, horizontal and vertical directions. The middle two layers are hidden layers provided with eight neurons in each. Number of neurons in each hidden layer is determined by trial and error method. From the experimental data, 30 samples were used to train the proposed network and 6 samples were selected randomly to test the data for the two bearings. Figs. 9 and 10 are the learning graphs for the bearings 1 and 2 respectively. The network was trained using feed forward back propagation algorithm. Easy NN plus software was used for training this network. During the training, weights between the connections were automatically selected by the software itself. The target training error was set to 0.01 and the training is stopped when the average training error was less than the target error. The network was trained at learning rate of 0.6 and momentum of 0.8. The red line is the maximum example error, the blue line is the minimum example error and the green line is the average example error. The orange line is the average validating error. Learning progress graph shows the maximum, average and minimum training errors. The average validating error is shown, if any, validating example rows are included editor@iaeme.com

10 Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks Figure 9 Learning progress graph with maximum, average and minimum training error (Bearing 1) Figure 10 Learning progress graph with maximum, average and minimum training error (Bearing 2) editor@iaeme.com

11 V Sudheer Kumar, Dr. CH Nagaraju and Dr. K Venkatrao Sample Number Table 3 Experimental and predicted values of frequency of shaft vibration for bearing 1 Depth In mm Speed Exp. Ax Value Ay Values Az Values ANN % error Exp. ANN % error Exp. ANN % error Mean Error 4.92 Mean Error 4.63 Mean Error 5.03 Sample Number Table 4 Experimental and predicted values of frequency of shaft vibration for bearing 1 Depth In mm Speed Exp. Fx Value Fy Values Fz Values ANN % error Exp. ANN % error Mean Error 4.14 Mean Error 2.62 Mean Error 2.48 Exp. ANN % erro r editor@iaeme.com

12 Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks Sample Number Figure 11 Amplitude (Experimental & ANN) and Frequency (Experimental & ANN) comparison Graphs for bearing 1 After training the network, the network was used to predict the responses for the both bearings. Predicted values of amplitude and frequency vibration are shown in Fig. 11 and 12 for Bearing 1 and bearing 2. Percentage of error between experimental values and predicted values for the vibration amplitude and frequency is calculated for both bearing 1 and 2. From the Tables 3 & 4 the Mean error percentage was found as 4.92%, 4.63% and 5.03% for amplitude vibration in axial, horizontal and vertical directions, 4.14%, 2.62% and 2.48% for frequency vibration in axial, horizontal and vertical direction for Bearing 1 and from Tables 5 & 6 the Mean error percentage was found as 3.31%, 4.60% and 6.10% for amplitude vibration in axial, horizontal and vertical direction, 4.18%, 3.04% and 3.12% for frequency vibration in axial, horizontal and vertical direction for Bearing 2. Table 5 Experimental and predicted values of amplitude of shaft vibration for bearing 2 Depth In mm Speed Ax Value Ay Values Az Values Exp. ANN % error Exp. ANN % error Exp. ANN % error Mean Error 3.31 Mean Error 4.60 Mean Error 6.10 Sample Number Table 6 Experimental and predicted values of frequency of shaft vibration for bearing 2 Depth In mm Speed Fx Value Fy Values Fz Values Exp. ANN % error Exp. ANN % error Exp. ANN % error Mean Error 4.18 Mean Error 3.04 Mean Error editor@iaeme.com

13 V Sudheer Kumar, Dr. CH Nagaraju and Dr. K Venkatrao Figure 12 Amplitude (Experimental & ANN) and Frequency (Experimental & ANN) comparison Graphs for bearing 2 From Fig. 11 and 12, it was found that the predicted values are very close to the experimental values. From these results, it can be deemed that the proposed network model is capable of predicting the amplitude and frequency of vibration editor@iaeme.com

14 Modeling and Characterization of Crack Depth on Rotor Bearing using Artificial Neural Networks 5. CONCLUSIONS In the present study, vibration characteristics of cracked steel shaft were studied at different speeds and depth of cracks on the shaft. Interaction effect of speed and crack depth on the responses was studied and predictive models for the responses were developed ANN. The following conclusions may be drawn from the work: At bearing 1, the irregular correlation among amplitude, crack depth and shaft speed was observed. It was observed that amplitude is rising gradually with speed and depth. The amplitude of shaft vibration was observed to be high at shaft speed of 500rpm and Crack depth of 2 mm. At bearing 1, it was also observed that a sudden rise correlation among frequency due to crack depth and shaft speed. It was observed that frequency is rising and lowering gradually with speed and depth. The frequency of shaft vibration was observed to be high at shaft speed of 1000 rpm and crack depth of 4mm. At bearing 2, Interaction effect of shaft speed and crack depth on amplitude shows that the amplitude is rising gradually with shaft speed and crack depth. At bearing 2, it was also observed that there is irregular correlation among frequency, crack depth and shaft speed. The frequency of vibration was found to be high at cracks depth of 4mm and 6mm and shaft speed of 1000 rpm. The proposed ANN models were training with feed forward back propagation algorithm and used to predict responses. It was found that the predicted values are very close to the experimental values. From these results, it can be deemed that the proposed network model is capable of predicting the amplitude and frequency of vibration. The authors declare that there is no conflict of interest regarding the publication of this paper. REFERENCES [1] Wauer J.,Modelling and formulation of equations of motion for cracked rotating shafts, International Journal of Solids and Structures, Vol. 26, 1990, PP [2] Christopher Torrence., and Gilbert P., A Practical Guide to Wavelet Analysis, Bulletin of the American Meteorological Society, Vol.79(1),1998, PP [3] Imam I., Azzaro S. H., and Bankarst R. J., Development of online rotor crack detection and monitoring system, Trans. ASME, Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol.111, 1989, PP [4] W.C. Foiles, P.E. Allaire and E.J. Gunter, Review: Rotor Balancing, Shock and Vibration, Vol. 5, No. 5-6, 1998, pp [5] Vibration-based identification of faults such as rotor imbalance, rotor bend, crack, rub, misalignment, or fluid induced instability, is well-developed. J.K. Sinha, Health Monitoring Techniques for Rotating Machinery, PhD Thesis, University of Wales Swansea, 2002 [6] Tejas H. Patel, Ashish K. Darpe. Vibration response of misaligned rotors, Journal of sound and vibration 325(3), 2009 pp [7] S. P. Mogal, D. I. Lalwani Experimental investigation of imbalance and misalignment in rotor bearing system using order analysis Journal of Measurements in Engineering. 3(4), 2015, pp [8] Joon Young Jang and Michael M. Khonsari Review On the Characteristics of Misaligned Journal Bearings lubricants 2015 Volume 3, pp editor@iaeme.com

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