本研究利用多重碎形理論作為訊號分析方法，用以解析高速滾珠螺桿機台運轉之訊號以達到失效分析之目的。利用單一碎形理論中的維度D_s值及高度尺度參數G值能反應出機台運轉時之狀態，但僅藉由此二碎形參數之趨勢變化所能得知的訊息仍屬有限。本文之特點為加入可描述碎形維度在空間或時間中分佈現象的多重碎形理論，以不同之尺度指數區分強弱訊號並顯示碎形維度分佈情形，許多現象便在此分類後再分析的過程顯示。本文之另一特點為運用多重碎形之概念進一步分析高度尺度參數，高度尺度參數原為運用於描述物體表面形貌之起伏，而後亦被運用在訊號分析中，多重碎形理論中並無高度尺度參數或類似之參數，本文嘗試以瞬時高度尺度參數分佈偏度係數作為分析方法，並得到其與能反映出潤滑油脂之溢漏狀況之結果。本文並針對高速滾珠螺桿機台之訊號特性加以分析，說明特定訊號如量測雜訊、球通訊號反應在多重碎形分析之特徵值。本研究之研究方法以建立軟體提供業界使用。
經多重碎形理論分析後，訊號在試件發生擦損前後顯示出明顯的差異，發生擦損後之訊號多重碎形頻譜曲線開口遠寬於發生擦損之前，反應出接觸行為較為不穩定，這是利用單一碎形理論分析時所無法觀察的。針對扭矩及振動訊號之多重碎形分析，在滾珠螺桿之軸承失效故障前確實能反映出異狀，在故障發生前三小時其多重碎形頻譜曲線開口亦越來越寬，反應其訊號越來越不穩定。多重碎形理論有潛力運用於複雜機構之機台之失效分析、預測，機械元件在失效前很可能產生些微的徵兆，並影響各種等訊號，多重碎形理論提供一個跨越尺度的角度來篩選、解析這些徵兆。

In this thesis, we use multifractal theory as a signal processing method to resolve the ball-screw signal to achieve failure analysis. Monofractal and topothesy can reflect the state of running machines, but there is only a few information we could get from those two values. One of the unique of this study is using multifractal theory which characterized the uneven distribution of monofractal in time or space, signal is discriminated by different Hölder exponent and then analyze fractal dimension respectively, some phenomenon was shown during those processes. Another feature of this study is to combine multifractal theory with topothesy. The original function of topothesy is characterizing the undulating of surface topography, then topothesy is used in signal process to represent the amplitude. But there is no topothesy or other similar parameters in multifractal theory, in this study, we analyze the distribution of instantaneous topothesy as a method to failure analysis.
The result of experiments shows huge difference between scuffing and non-scuffing after analyzed by multifractal theory, which can not show in monofractal analysis; multifractal analysis of vibration and torque signal can reflect the condition of ball-bearing failure, those cases show that it is potentially to use multifractal theory to failure analysis. We also describe the character of ball-screw signal, identify how the specific signal such as ball-pass signal and noise show in multifractal spectra.

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