Four Dimensional Holospectrum—A New Method for Analyzing Force Distributions

[+] Author and Article Information
R. Du, Yue-Dong Chen

Department of Industrial and Manufacturing Systems Engineering, University of Windsor, Windsor, Ontario, Canada

Yubao Chen

Department of Industrial and Manufacturing Systems Engineering, University of Michigan, Dearborn, Dearborn, Michigan U.S.A.

J. Manuf. Sci. Eng 119(1), 95-104 (Feb 01, 1997) (10 pages) doi:10.1115/1.2836560 History: Received December 01, 1994; Revised November 01, 1995; Online January 17, 2008


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.

Copyright © 1997 by The American Society of Mechanical Engineers
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