1. A Study on the Exponential Decay for the Bearing Defect Diagnosis 沈毓泰 南台科技大學 機械系 教授

2. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 2 Signal processing for bearing defect vibration typical of amplitude modulation 1. Introduction A single mode vibration

3. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 3 2. High frequency resonance technique The traditional signal processing band-pass filter  rectifier  low-pass filter The demodulated single

4. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 4 3. Mechanical vibration analysis The vibration signal with amplitude modulation for the bearing vibration

5. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 5 The vibration signal for the lth mode vibration would be i : the sampling point of the bearing vibration f s : the sampling frequency j : the interval number of the envelope signals

6. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 6 the number of data points is h over the j th half period 4.The envelope estimation

7. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 7 The solution obtained in a linear least squares sense would be The envelope signal would be

8. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 8 The inner-race defect case

9. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 9 The advantages the envelope estimation algorithm could theoretically retrieve several envelope signals corresponding to their mode vibrations and the envelope signals are less distorted. the envelope signals would automatically become low-sampling-rate signals.

10. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 10 it is easy in calculation to retrieve the envelope signals from a modulated vibration or even to reconstruct the modulated vibration from the envelope signals.

11. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 11 5. The estimation of exponential decay The envelope of an impulse response in the time interval,  t, could be expressed as with and would be rewritten as

12. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 12 where The solution for  l and ln( C lm )

13. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 13 5 、 Experimental Result Resonance mode  Bearing type First resonance mode Second resonance mode Third resonance mode Normal2025751430 Outer-race defect58711272332 Inner-race defect59412192721 Roller defect48611592054 Multiple defect44112161910 The exponential decay for the envelope signals at running speed 800 rpm

14. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 14 Resonance mode  Bearing type First resonance mode Second resonance mode Third resonance mode Normal1163991033 Outer-race defect58211152934 Inner-race defect58712442798 Roller defect58112212640 Multiple defect43812872278 The exponential decay for the envelope signals at running speed 1600 rpm

15. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 15 6 、 Conclusion an envelope estimation algorithm is carried out to retrieve the envelope signals from the corresponding resonance modes. the diagnosis index based on the exponential decay is proposed and proved effective in monitoring the bearing running condition.

16. 2007/ 5/ 19 南台科大 訊號處理與機械診斷實驗室 16 Thank you