Nonlinear periodic response analysis of mechatronic systems with friction

Nonlinearities are present in many coupling components of mechanical and mechatronic systems, with the most common nonlinear coupling property being that of friction force. Transient simulation of systems with nonlinear friction can be a challenge in terms of solver robustness and calculation time. Moreover, many manufacturing processes lead to periodic forces and motions such as in milling, or repetitive pick-and-place serial production operations. In this paper, a method and application for nonlinear periodic response analysis (NPRA) of reduced-order mechatronic systems is presented, which leverages the fact that the majority of components in common mechatronic systems (e.g. machine tools) are linear. The dynamic behaviour of these components can thus be represented using a linear reduced order model (ROM). The analysis is implemented using the Harmonic Balance Method (HBM), which is then applied to the ROM of a simple, structurally compliant mechatronic system with a motion controller and profiled rail guideways. A practical case encountered in industrial settings is analysed, that being the testing of a system's frequency response. Periodic responses to a harmonic velocity setpoint input oscillation are analysed in both time and frequency domains and comparisons then made between measurement and simulation. This comparison shows that many significant effects of nonlinear friction in ROMs of mechatronic systems can be modelled using the NPRA method and a simple friction model with a presliding regime. The combination of HBM with model order reduction (MOR) opens up afield of applications for the efficient and robust simulative analysis of periodic processes with nonlinear couplings in complicated mechatronic systems.