No abstract

This paper presents an improved scheme based on the frequency response functions (FRFs) for in-situ identification of joint parameters of mechanical structures. Despite that measurement of FRFs at joint locations is essential for identifying the joint parameters of a structural dynamic system, it is often impossible to measure FRFs at joint locations. To this end, the present paper suggests an indirect estimation technique for unmeasured FRFs which are required for identification but not available. Theoretical investigation is made to delineate the effects of measurement noise and modeling error on indirect estimation and identification. Two index functions are introduced, which can indicate the quality of estimation or identification along the frequency. The index functions are proven to be useful not only as a weighting function in the identification procedure but also for evaluating the frequency region appropriate for identification. A series of simulations as well as experiments are performed for validation of the method.

In-situ identification is essential for estimating bearing joint parameters involved in spindle systems because of the inherent interaction between the bearings and spindle. This paper presents in-situ identification results for rolling element bearing parameters involved in machine tools by using frequency response functions (FRF’s). An indirect estimation technique is used for the estimation of unmeasured FRF’s, which are required for identification of joint parameters but are not available. With the help of an index function, which is devised for indicating the quality of estimation or identification at a particular frequency, the frequency region appropriate for identification is selected. Experiments are conducted on two different machine tool spindles. Repeatable and accurate joint coefficients are obtained for both machine tool systems. [S0022-0434(00)02501-6]

The present paper proposes an in situ modal parameter-based method for determining the dynamic joint characteristics of mechanical systems. The proposed method uses the mass, damping and stiness matrices of the structure, calculated by the ®nite element method (FEM), along with measured eigenvectors and eigenvalues of the actual system. While the modal parameters at the joint must be known in order to identify the structural joint dynamic characteristics, it is often impossible to measure the response of the system directly at the joint location. To overcome this problem and eliminate the errors associated with using measurements close to the joints, an alternative indirect estimation scheme is used to determine the complete set of eigenvectors, and thus the eigenvector component corresponding to the joint location is extracted. Therefore, the proposed method allows in situ joint parameter identi®cation. The eciency of this method is validated by simulations with dierent mechanical systems, and the robustness is also demonstrated with errors introduced into the estimated eigenvectors. Finally, the method is implemented for experimental identi®cation of the joint parameters of an actual spindle system. NOTATION c nn linear damping coecient of the nth joint C J joint damping matrix C c J condensed joint matrix C o damping matrix excluding joint parameters C c o condensed damping matrix excluding joint parameters D J ! dynamic stiness matrix for the joints D o ! dynamic stiness matrix for the structure excluding the joints E i error vector associated with the equation of motion for the ith mode f force vector k nn stiness coecient of the nth joint K J joint stiness matrix K c J condensed joint stiness matrix K o stiness matrix excluding bearing joint parameters K c o condensed stiness matrix excluding bearing joint parameters m number of modes M o mass matrix excluding joint parameters M c o condensed mass matrix excluding joint parameters q coordinate vector q e vector of the excitation coordinates (of order e) q m vector of measured coordinates (of order m) q " m vector of the unmeasured coordinates (of order " m) q n vector of the coordinates connected to the bearing joints (of order n) q " n vector of the coordinates not related to the bearing joints (of order " n) T i transformation matrix to extract the coordinates associated with subscript i u right latent vector left latent vector ! eigenvalue % square error function w i eigenvector of the ith mode Subscripts J joint o structureThe MS was