A family of substructure decoupling techniques based on a dual assembly approach

Predicting mobile machine tool dynamics by experimental dynamic substructuring

“…Low coherence in measured FRFs further contributes to errors observed at the low frequencies. Discrepancies may also be attributed to decoupling being sensitive around the anti-resonances of the known subsystem(s), and to coupling being sensitive around the resonances of the subsystems [17]. Local high-frequency modes in the 650 -1200 Hz range belonging to the spindle and tool-tool-holder combination are better approximated since these are less affected by observability/controllability issues at the coupling points.…”

“…(3) can be rewritten compactly using a Boolean matrix description as: [17], which requires that compatibility and equilibrium be satisfied only at the interface DoFs between subsystem B 1 and the assembled system AB 1 .…”

“…Employing the dual formulation for decoupling [17], the interface forces are satisfied a priori by choosing the interface forces of the form of: 6 (7)  gB λ T wherein λ are Lagrange multipliers, corresponding physically to the interface force intensities. The equilibrium conditions in Eq.…”

“…3 Decoupling to extract dynamics of the complete machine that are to be subsequently coupled to other substructures, as is considered in this paper, is new. Methods described in this paper build on our preliminary simulation based substructure (de)coupling work [15][16], and are thought to be novel extensions and applications of otherwise well-developed FBS methods [7,17]. only; A -extracted mobile machine tool; B 2 -second base type; AB 2 -mobile machine coupled to the second base type.…”

General Formulation of Inverse Substructuring Method for Multicoordinate Coupled System

“…To circumvent ill-conditioning around particular frequencies, D' Ambrogio [9] provided a dual domain decomposition method by adding a fictitious subsystem, which is the negative of the residual subsystem, to the coupled system. Most recently, Voormeeren and Rixen [10] presented a so-called dual approach to substructure (dis)assembly which allows imposing different equilibrium and compatibility conditions during decoupling in both the physical and modal space.…”