# Mathematical Model of Spindle Unit Bearing Assembly

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

## Abstract

The mathematical model which links an information signal with the parameters of technical state of mechanical node in the best way will allow developing methods for diagnosing emerging defects at the operational stage. Development of a mathematical model of spindle unit bearing assembly, which would analytically describe the mechanism of vibration signal formation, linking it to the parameters of the technical state, is a relevant objective at the present time. Perhaps, such a mathematical model will effectively apply the Huang–Hilbert transform to vibration signals, using adaptive decomposition of signals into physically significant components, and also improve the efficiency of currently used analysis methods. The obtained mathematical model qualitatively determines the mechanism of the frequency composition of the vibration spectrum appearing, takes into account the microgeometry of the raceway and ball profiles, when the radial (angular contact) ball bearing works, and gives a quantitative estimate, the error of which will largely depend on the signal/interference ratio of the experimentally obtained time implementation of vibration acceleration (vibration displacement).

## Keywords

Mathematical model Spindle unit Huang–Hilbert transform Vibration signal Ball bearing Contact deformation

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