In this paper, a new method, called four dimensional (4D) holospectrum, is introduced for analyzing force distributions. First, it is shown that the dynamics of a three dimensional force can be represented by the holospectrum, which consists of a series of ellipses in a three dimensional space with each ellipse representing the frequency characteristics of the force at a concerned frequency. An ellipse can be described by its normal vector, major axis, minor axis, eccentric ratio, area, and inclination angle. The formula of calculating these quantities are derived next. 4D holospectrum reveals the dynamic characteristics of a three dimensional force such as phase and spatial correlation that cannot be accessed otherwise. As demonstrated by the experimental tests on a spindle, 4D holospectrum adds a new dimension for force analysis and is very valuable for on-line monitoring and diagnosis as well as design.

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