An in situ modal-based method for structural dynamic joint parameter identification

Abstract

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

A Numerical Model to Predict Damaged Bearing Vibrations

“…Some authors investigated bearing-support models, with more detailed models used for adjoining systems (supports, spindles, etc. )1 in some cases however, less detailed bearing models were used (Shamine et al, 2000). Other researchers simply studied bearing-induced vibration without transmission phenomena (Spiewak and Nickel, 2001).…”

Surface fractal topography-based contact stiffness determination of spindle–toolholder joint

“…For the drawbar force, we choose F d ¼ 12 kN as the typical condition. Based on the dimensions of the joint, the nominal area can be easily obtained from equation (2). The normal contact surface of spindletoolholder joint is A a ¼ 7:49 Â 10 À3 m 2 .…”

“…The contact behavior of joint surfaces plays an important role in the stiffness and damping of the assembly of toolholder and spindle, directly contributing to the dynamic characteristics of the high speed machine tools. [1][2][3] High performance of spindle-toolholder joints becomes increasingly significant contribution for machine tools.…”