應用小波能量密度分析於軸承損壞之模態振動研究

A Study of Applying Wavelet-based Energy Density Analysis on the Modal Vibration of Bearing Defect

本文提出模糊決策分析法則應用於無線生理檢測系統，在使用者身上配置無線生理感測模組及行動裝置(PDA)，利用無線生理訊號感測模組蒐集各種生理訊號，如：心電圖、心跳、心率變異度及自律神經活性等。所蒐集的訊號經藍芽串列傳輸傳送至行動裝置，提供即時檢測及儲存功能。利用行動裝置的無線網路功能連結遠端的伺服器，以自律神經的成人標準建議值做為模糊理論之歸屬函數設定依據，並使用模糊理論在生理資訊與資料庫病史的分析上。分析結果可以提供被觀測者身體的緊張及疲勞等健康資訊，使所獲得的生理數據得以更為淺顯易懂以及給予使用者適時的警示，而家屬及醫生則可利用遠端查詢功能達到行動醫療照護目標。本系統可以擴展至醫院與居家照護之需求，利用行動生理檢測系統，整合無線區域網路技術，跳脫醫院及居家等區域，達到無所不在之行動監控應用。在本研究中，以Morlet小波應用於軸承模態振動之能量密度分析。由於機械系統之振幅調變訊號，可利用Morlet小波經由設定適當之參數，以濾出單一模態之振動訊號，其模態振動能量則可藉由小波變換之能量守恆特性來獲得，並且為模態振動的平方；因此模態能量密度可表示為時間的函數，而其模態能量頻譜則可用於診斷軸承損壞。由理論與實驗探討證實，小波能量密度分析可有效地解析軸承損壞特性，並且藉由此模態能量密度函數之模態能量頻譜可清楚呈現損壞特徵頻率。

In this paper, the Morlet wavelet is studied so that it can be applied in energy density analysis for the modal vibration of bearing defects. It is shown that the vibration signal with amplitude modulation of a mechanical system can be filtered out of one of the resonance modes through the Morlet wavelet if the parameters are properly designated. The modal vibration energy can be derived from the isometric properties of the wavelet transformation, and will be the square of the modal vibration. Accordingly, the energy distribution of the bearing vibration can be expressed as a function of time in this modal vibration, and the modal energy spectrum can be applied in diagnosing the bearing defects. According to the theoretical and experimental studies, it is shown that the wavelet-based energy density analysis can effectively extract the defects and, thus, the modal energy spectrum can clearly show the defect characteristic frequency from the modal energy density function of roller bearings with defects.