Mathematical model of capacitance micromechanical accelerometer in static and dynamic operating modes

Monitoring and early diagnosis systems, on which the protection function of both hydroturbines and auxiliary power equipment rely, are becoming increasingly relevant. One of the most promising methods of technical control and diagnostics of hydo units is the analysis of their vibro-acoustic characteristics. But a significant technical problem that arises in the construction of such systems is the limited use of known sensors of vibration velocity and vibration displacement due to the fact that the rotary speed of hydro units is usually below the lower limit of operation of sensors of this type. One of the promising ways to solve this problem is using capacitive micromechanical accelerometers. However, the existing mathematical models describing this type of accelerometers have low accuracy, which limits their practical using. The mathematical models of the capacitive micromechanical accelerometer for static and dynamic modes of operation are developed in this article. It was established that this accelerometer has a constant sensitivity, therefore its static characteristic is linear. It is shown that in the dynamic mode of operation of a capacitive micromechanical accelerometer has a dynamic error component, the cause of which is its own displacement of the moving part of the sensor, which is due to the inertial properties of the moving part and elastic properties of stretch marks. The mathematical dependence of the absolute dynamic error of the capacitive micromechanical accelerometer is obtained, the removal of which from the measurement results will improve the accuracy of the specified primary measuring transducer.