A Multilongitudinal Mode Quadrature Laser Self-Mixing Vibration Sensor for Fault Diagnosis of Bearing

We theoretically propose and experimentally demonstrate a simple and compact approach for the first generation of multilongitudinal mode quadrature laser self-mixing (MQLSM) vibration sensor. This is achieved by constructing two polarized self-mixing (SM) signals with adjustable phase shifts in multilongitudinal mode (MLM) lasers, leveraging the inherent characteristics of MLM spacing. It is found that, in the prescribed MQLSM vibration sensor, a pair of SM signals with quadrature phase difference can be retrieved on demand by resorting to the quadrature-phase construction algorithm together with a circle fitting process, which makes the target vibration accessible based on the related quadrature demodulation method. More impressively, our proposed MQLSM sensor's utility is exemplified in fault diagnosis of bearings as a proof of concept. Experimental results indicate that the vibration measurement error is less than 40 nm at a vibration amplitude of 5.00~\mu \text{m} and the measurement relative error of the characteristic frequency of fault bearing is less than 0.65%, thus enabling high-accuracy, compact, and robust MQLSM sensor. The findings presented here may hold extensive potential applications in online measurement, dynamic performance analysis, and beyond.