Derivation of Sensor-Actuator Layout for Active Control of Gearbox Housing Vibration

Abstract To effectively control the vibration of a complex structure like the housing of an automotive gearbox, a distributed network of point sensors and actuators is required. This work focuses on demonstrating optimal sensor and actuator placement concepts for industrial applicability for high frequency vibrations caused due to gear whine phenomenon. The goal is to minimize the transfer of vibration from gearbox housing to the car body through the structural connection points. The frequency domain of interest is 1000–5000 Hz. A network of 10 spatially distributed sensors is derived using the constrained Frequency Effective Independence method (FEfI) that maximizes the system observability of the housing vibration. In addition, an optimized two-actuator network is derived based on the concept of spatial and modal controllability in the frequency domain of interest. The study uses Frequency Response Functions (FRFs) of the gearbox housing obtained from an experimentally correlated finite element analysis. The sensor-actuator layout is tested in closed-loop simulation with the excitation using a multi-channel Filtered-X Least Means Squares (FxLMS) adaptive algorithm. The goal is to mitigate structure-borne vibration transfer from the gearbox housing at the mounting points. The derived optimal actuator layout is compared against a fully collocated actuator-sensor system. The design requirements for optimally positioned actuators can also be derived for the desired frequency domain.