Indirect Inverse Substructuring Theory for Coupling Dynamic Stiffness Identification of Complex Interface Between Packaged Product and Vehicle Transport System

Abstract

Inverse substructuring method has been recently proposed and applied for inverse analysis of the dynamical response of product transport system. The component-level frequency response functions (FRFs) and the coupling dynamic stiffness for facilitating the cushioning packaging design are all predicted from only the system-level FRFs. However, the system-level FRFs from coupling degree of freedoms may not be measured accurately because of the difficulties of vibration excitation and response measurement for the coupled interface between packaged product and vehicle within the limited accessible space. The aim of this paper is to develop a new FRF-based indirect inverse substructuring method for the analysis of the dynamic characteristics of a three-substructure coupled product transport system without measuring system-level FRFs at the coupling degree of freedoms. By enforcing the dynamic equilibrium conditions at the coupling coordinates and the displacement compatibility conditions, a closed-form analytical solution to inverse sub-structuring analysis of multi-substructure coupled product transport system is derived based on the relationship of easy-to-monitor component-level FRFs and the system-level FRFs at the coupling coordinates.. The proposed method is validated by a lumped mass-spring-damper model, and the predicted coupling dynamic stiffness is compared with the direct computation, showing exact agreement. Then, the FRF tests of a physical prototype of multisubstructure coupled product transport system are performed to further check the accuracy of the suggested method. The method developed offers an approach to predict the unknown coupling dynamic stiffness from measured FRFs purely. The proposed method may help to obtain the main controlling factors and contributions from the various structure-borne paths for product transport system.

Inverse Sub-structuring Method for Multi-coordinate Rigidly Coupled Product Transport System based on a Novel Shearing Probe Technique

“…To address this issue, an indirect inverse sub-structuring method was proposed. 11 Instead of using only system-level FRFs, the indirect method suggested to obtain the coupling stiffness and component FRFs from that of easy-to-monitor degree of freedoms (DOFs), which would avoid the difficulties of vibration excitation and measurement because of space limitation. Furthermore, the dummy mass method 12 and the probe technique method 13 were suggested recently to perform an inverse analysis of the product transport system, of which the probe technique method has great privilege in engineering applications due to the flexibility of the probe, and the negative effect of which can be easily eliminated, as claimed by the authors.…”

“…However, the difficulty to measure the needed FRFs at the coupling interface between packaged product and vehicle due to the limited accessible space has become the major challenge. To address this issue, an indirect inverse sub‐structuring method was proposed . Instead of using only system‐level FRFs, the indirect method suggested to obtain the coupling stiffness and component FRFs from that of easy‐to‐monitor degree of freedoms (DOFs), which would avoid the difficulties of vibration excitation and measurement because of space limitation.…”

Inverse Sub‐structuring Method for Rigidly Coupled Product Transport System based on Frequency Response Function Testing Probe Technique

“…To address this issue, an indirect inverse substructuring method was proposed. 19 Instead of using only system-level FRFs, the proposed method aimed to obtain the coupling stiffness and component FRFs from easy-to-monitor DOFs, which would avoid the difficulties of vibration excitation and measurement because of space limitation.…”

“…However, the system‐level FRFs from coupling DOFs, which were needed in previous inverse sub‐structuring methods, may not be measured accurately because of the difficulties of vibration excitation and measurement for the coupled interface between components within the limited space. To address this issue, an indirect inverse sub‐structuring method was proposed . Instead of using only system‐level FRFs, the proposed method aimed to obtain the coupling stiffness and component FRFs from easy‐to‐monitor DOFs, which would avoid the difficulties of vibration excitation and measurement because of space limitation.…”

Inverse Sub‐Structuring Theory for Coupled Product Transport System Based On the Dummy Masses Method

“…Although the inverse sub‐structuring method can predict the component‐level FRFs and the coupling dynamic stiffness from only the measured system‐level FRFs, facilitating much the cushioning packaging design process, the system‐level FRFs from coupling degrees of freedom may not be measured accurately because of the difficulties of vibration excitation and/or response measurement for the coupled interface between packaged product and vehicle within the limited accessible space. To overcome this difficulty, Wang J. and Lim recently suggested an indirect inverse sub‐structuring method. However, according to the indirect inverse sub‐structuring method, both of the system‐level FRFs and parts of the component‐level FRFs should be measured before applying the method, which brings three problems: (a) First, the components may behave differently in free state compared with that in coupled system.…”