A modal momentum method for the identification of structural weak links

In order to meet the demands of weak-link identification of mechanical structures in high-precision equipment, this paper introduces the concepts and equations of modal momentum and modal momentum difference ratio (MMDR), as well as an identification method of weak links based on modal momentum. In this method, the modal data of the mechanical structure is acquired first through experimental modal analysis or finite element analysis. The modal momentum of each measured point is calculated based on the modal data and transformed to the global coordinate system. Then, the MMDRs between the measured point with the largest magnitude of modal momentum and its adjacent measured points are calculated. Weak links are judged if the MMDR exceeds a predefined threshold. Twelve different multi-degrees-of-freedom systems incorporating weak links were designed and then identified using the proposed method. The accuracy of identification is up to 100% for these systems. The method was applied to a double pendulum angle milling head of a five-axis numerically controlled machine tool, and the result reveals that the side plate lacks bending stiffness.