Non-simultaneous real-time hybrid simulation of a numerical and experimental mechanical system with moderate nonlinearities via iterative coupling based on Frequency Response Functions

The coupled simulation of numerical and real subsystems is sometimes called ‘hybrid substructuring’, ‘hardware in the loop (HIL)’, ‘cyberphysical simulation’, or ‘hybrid simulation’, and is an active field of research. In this publication, an iterative algorithm for a coupled simulation of a numerical subsystem and a real (experimental) one is presented. The term ‘iterative’ means that the subsystems are not computed or tested simultaneously but in loops one after the other. After each loop run, new control signals are computed so that the deviation of the coupling forces and displacements becomes smaller with each iteration. If the coupling quantities are equal, then the systems are coupled in a mechanical sense because of the cutting force principle. The proposed method works for quasi-static (slow speed) and dynamically reacting systems as well as for subsystems with moderate nonlinearities. The iterative character has several consequences: (1) No controllers are necessary. (2) The speed of the data exchange is not critical. (3) The method can only be applied to components whose properties do not change during the simulation (e.g. due to damage). Privacy between the two domains is guaranteed, as no explicit mathematical models in the sense of Finite Element (FE) structures or the like, but only frequency response functions, have to be exchanged. A possible application scenario could look as follows: An original equipment manufacturer (OEM) provides a web interface to a complex overall simulation model. A (geographically distant) supplier starts an iterative co-simulation with a somehow modified component (e.g. a bearing). Both sides can thus estimate the impact on the overall system. After explaining the theory, two examples are presented. The first concerns the coupled simulation of two pure numerical systems. In the second example, mixed numerical and experimental subsystems are coupled. Hence, a simple wheel suspension is considered, where the shock absorber is the real part on a test bench.