Using Residual Flexibility for Improved Observation of Reaction Forces in Flexible Structures

Abstract

This paper focuses on developing a full-state observer that can be used to obtain unmeasurable reaction forces in a flexible structure. In the context of modal truncation of a distributed parameter system, accurate representation of reaction forces is discussed and is shown to require a more comprehensive model than for displacement representation. This fact, coupled with the difficulty in directly measuring reaction forces in many applications points to the need for accurate estimation of ferees with reduced-order models. The residual flexibility, a term from past literature, is used to recapture some of the lost force information in a truncated model. This paper presents numerical and experimental results of a study where the residual flexibility is used in conjunction with a Kalman filter so that accurate force information may be obtained from a small set of displacement measurements with a reduced-order model. The motivation for this paper is to be able to obtain accurate information about dynamic bearing loads in a rotating machine for diagnostic and control purposes.