4-DIMENSIONAL HOLOSPECTRUM - A NEW METHOD FOR ANALYZING FORCE DISTRIBUTIONS

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 t he holospectrum, which consists of a series of ellipses in a three dim ensional space with each ellipse representing the frequency characteri stics of the force at a concerned frequency. An ellipse can be describ ed by its normal vector, major axis, minor axis, eccentric ratio, area , and inclination angle. The formula of calculating these quantities a re derived next. 4D holospectrum reveals the dynamic characteristics o f a three dimensional force such as phase and spatial correlation that cannot be accessed otherwise. As demonstrated by the experimental tes ts on a spindle, 4D holospectrum adds a new dimension for force analys is and is very valuable for on-line monitoring and diagnosis as well a s design.