Multi-DoFs nonlinear joint identification through substructure decoupling

Nonlinear joint identification is essential for predicting the dynamic behavior of complex mechanical systems with localized nonlinearities at the joint. The FRF Decoupling Method for Nonlinear Systems (FDM-NS) characterizes nonlinear joints by removing the linear dynamics of the connected subsystems from the nonlinear ones of the assembly. However, FDM-NS is only applicable to systems where the nonlinearity can be modeled as a single nonlinear elastic element connecting a pair of DoFs, and requires direct response measurements at these DoFs. This paper proposes an extension of FDM-NS to systems where the joint can be modeled as a single multi-DoFs element where several DoFs may exhibit nonlinearity, and overcomes the need of direct measurement at the joint DoFs which are in general inaccessible. The proposed method introduces the Virtual Point Transformation (VPT) into the FDM-NS. The VPT is used in real-time during measurements to obtain the relative displacement between the pairs of joint DoFs that exhibit nonlinearity. This enables controlling (i.e., fixing at a constant level) the relative displacement of a pair of nonlinear joint DoFs and obtaining the corresponding quasi-linear FRFs of the assembly needed for FDM-NS. The potential and limitations of the proposed method are investigated using experimental measurements on a laboratory testbed containing a multi-DoFs nonlinear joint. It is found that controlling only one pair of joint DoFs ensures that the relative displacement of the other pairs of nonlinear DoFs is effectively fixed during the measurements. The results show that the proposed method can correctly identify joints that can be modeled as a single multi-DoFs nonlinear element whose DoFs are inaccessible for measurements.