Difference Spectrum Theory of Singular Value and Its Application to the Fault Diagnosis of Headstock of Lathe

Abstract

It's proved that signal can be decomposed into the linear sum of a series of components by singular value decomposition (SVD) when Hankel matrix is used. In order to determine the proper number of useful components,the concept of difference spectrum of singular value is put forward. Difference spectrum can effectively reflect the difference of singular values of the useful components and noise ones,and the number of useful components can be determined according to the peak position in the difference spectrum. The research results show that if the maximum peak is in the first coordinate,it means that a major direct current component exists in the signal and under this circumstance the number of useful components will be determined by the second maximum peak position,otherwise the number of useful component is determined by the maximum peak position. The influence of Hankel matrix structure on noise reduction effect of SVD is studied by dint of difference spectrum and it's pointed out that there exits a parabolic symmetry relationship between matrix column and noise erasing amount. On these bases this method is applied to the processing of turning force signal and the modulated signal caused by the gear vibration in the headstock is isolated successfully,furthermore the fault gear is located reliably according to this isolated signal.