Determination of shaft rotation angle from accelerations of the wireless sensor by the novel numerical method

The scheduled maintenance allows us to prevent breakdowns and unplanned downtime of equipment but limits the flexibility of manufacturing systems. On the other hand, condition monitoring concept enhances the manufacturing systems flexibility but requires reliable diagnostic information in real-time. Modern technologies, e.g., wireless power and Industrial Internet of Things (IIoT), allow implementing high-sensitivity sensors such as the Wireless Acceleration Sensor (WAS) for condition monitoring. The WAS is mounted on a machinery rotating shaft and the WAS measures angular, linear accelerations and angle of the shaft simultaneously. Moreover, the WAS contains a high-performance microcontroller, which allows processing measured data and estimating machinery condition in real-time. However, the accuracy of the angle measurement by the WAS significantly affects the accuracy of linear accelerations measurement by the WAS. In this paper, the authors propose the novel numerical method which allows us to measure accurately of a rotation angle and linear accelerations of the shaft. The method is based on a regularization technique and application of finite-difference equations. Besides, the study shows the results of simulation at applying the numerical method to calculate the rotation angle of the shaft using measurement data, which contain noise, obtained from the wireless accelerations sensor. The simulation results show that the numerical method effectively determines the rotating angle and the method is robust to noise.