1. ANALYSIS OF VIBRATIONSIGNALS TO IDENTIFY CRACKSIN A GEAR UNIT USING WAVELET TRANSFORMSUNDER THE GUIDANCE OFB. A. SUJATHA KUMARI SUSHANTH JASST PROF, DEPT of E&C 4JC09LIE18SJCE, Mysore INDUSTRIAL ELECTRONICS SJCE, Mysore1

2. WHAT SHALL WE KNOW ABOUT INTRODUCTION TO CRACK DETECTION DATA ANALYSIS METHODS AND TECHNOLOGYUSED DESIGN AND IMPLEMENTATION RESULTS CONCLUSION AND FUTURE ENHANCEMENTS REFERENCES 2 3. INTRODUCTION TO CRACK DETECTION Vibration analysis is important tool for faultidentification. 3 4. Signals in practice, are TIME-DOMAIN signals in theirraw format. Mathematical transformations are applied to signals toobtain a further information from that signal that isnot readily available in the raw signal. 4 5. REVIEW OF DATA ANALYSIS METHODS TIMEDOMAINANALYSIS FOURIER TRANSFORMS FREQUENCY Butterfly algorithm Bluestein algorithmDOMAIN STFT WAVELET TRANSFORMSANALYSIS CWT DWT 5 6. Fourier Transforms The frequency spectrum of a signal shows what frequencies exist in the signal BUTTERFLY ALGORITHMBLUESTEIN ALGORITHM Highly efficient Used for Prime sizes Computation time is less Reduces memory requirement Cannot be used for prime sizes 6 7. Continuous Wavelet Transforms CWT was developed as an alternative approach tothe STFT to overcome the resolution problem. CWT gives good time resolution and poorfrequency resolution at high frequencies and goodfrequency resolution and poor time resolution atlow frequencies. The width of the window is changed as thetransform is computed for every single spectralcomponent.7 8. At s = 1At s = 5At s = 208 9. WAVELET BASIS - MORLET Morlet wavelet, which is a complex sinusoid windowedby a Gaussian function. Mother wavelet Real part Imag part 9 10. TECHNOLOGY USED C# an object oriented programming language.I.C# does not allow multiple inheritance or use of pointers.II. Power of the C# programming language, combined with thesimplicity of implementing Windows Form applications in VisualStudio .NETIII. Versatile and flexible tool for creating Charts, graphics, andgraphical user interfaces. Common language Runtime Framework layer that resides above the OS and handles the execution of all the .Net applications. Microsoft Intermediate Language When we compile our .Net Program our source code does not get converted into the executable binary code, but to an intermediate code10 11. TECHNOLOGY USED Just in time compilers Compiles the IL code to native executable code(.exe or .dll). The Visual Studio .NET IDEI.Keyword and syntax highlighting.II. Solution explorer helps us to manage applications consisting ofmultiple files.III. Building user interface with simple drag and drop support.IV. Properties tab that allows setting different properties for multiplewindows controls.V. Standard debugger that allows us to debug our program usingputting break points for observing run-time behavior. WinForms and Win ApplicationsI. Windows applications are event driven.II.A windows form may contain text labels, push buttons, text boxes, list boxes, images, menus and vast range of other controls.III. all windows controls are represented by base class objects contained in the System.Windows.Forms namespace.11 12. DESIGN AND IMPLEMENTATIONShaft rotational The Five Basic Frequencies frequency( fs ) Fundamental trainfrequency( fFTF ) Ball pass outer raceway frequency( fBPOF ) Ball pass inner racewayfrequency( fBPIF ) Ball rotational frequency( fB )12 13. n = number of samples Input fs = Input frequency = 1/(speed in rpm) Dc = cage diameter in inches Db = ball diameter in inchesParameters Theta = Contact angle of bearing Nb = Number of balls 13 14. Damage detection using FFT We construct basic frequency amplitude vectors torepresent different bearing vibrations. These vectors are created from the power spectrum ofthe vibration signal and consist of the five basicfrequencies; with varying amplitudes based on thedefect present. Since the spectral components near the five basicfrequencies are also important, when generating thevector we consider a frequency band of 1OHz for eachbasic frequency 14 15. Time taken for the inner/outer race to rotate onerevolution time = (1 / fs)Condition - Inner Race Running(fi= fs, fo=0) Time for the inner race ball frequency ie time_inner_outer = Math.Round((1 / fBPIF),5); Number of balls that pass over the defect eachrevolutionie ball_passes = (time / time_inner_outer); Percentage of the balls are passing over a point onthe outer race each revolution.ie ballpass_Percentage = (ball_passes / Nb) * 100;15 16. Condition - Outer Race Running(fi= 0, fo=fs) Time for the inner race ball frequency ie time_inner_outer = Math.Round((1 / fBPIF),5); Number of balls that pass over the defect eachrevolutionie ball_passes = (time / time_inner_outer); Percentage of the balls are passing over a point on theouter race each revolution.ie ballpass_Percentage = (ball_passes / Nb) * 100;16 17. The basic frequency amplitude vector Frequency band = [f-5, f+5], where f= basic freqie f can be fs, fFCF, fBPO, fBPIF, fB. Where P = weighted sum of spectral magnitude Accordingly 5 basic frequencies are calculated for both normal and abnormal conditionsThe Basic frequency amplitude vector Damage percentage can be calculated usingX(f) %= [( X(f)normal X(f)abnormal )/ X(f)normal ] *10017 18. Damage detection using wavelettransforms For each scale factor s, it creates a real & Complex wavelet whoseperiod is that many samples long. The morlet wavelet that is used is a cosine function multiplied by aguassian(For real part) and with sine multiplied by a guassian(for imagpart) Once wavelets are created, it convolves the wavelet with the signal. To speed up the algorithm, convolution is done by multiplying Fouriertransform of the signal and the Fourier transform of the wavelet. After the convolution we end up with the strength of wavelet in thesignal at each point in time. Process is repeated for each scale value starting from 2 upto samplelength in steps of 2n. We will get real and complex data samples. Their magnitudes aretaken and plotted.18 19. STARTMultiply the contents of buffer B1 and B2 point wise and store it in Load the input signal and buffer B3 sample the input N of anydesired frequencyPerform IFFT on buffer B3 and storeit in buffer B4 which gives theInitialize buffers B1, B2, strength of the wavelet. B3 and B4Perform FFT on the input signal Check if scaleandS