Mathematical Model for Measuring Transformation of Vibration Displace-ment by Capacitive Sensor into a Time Interval

Abstract

In accordance with the international research experience, the maximum allowable normalized vibration displacement values for each group of machines from 15 kW to 500 MW to their respective vibration state are given. The importance of determining the nature of the vibration signal and choosing the appropriate tools for its evaluation is formulated.

The analysis of the sequence of the conversion of the vibration displacement into the output voltage by a capacitive sensor, which has a long measuring circle and therefore a large error compared to the direct measurement conversion of the vibration displacement into a time interval, was carried out.

Structural diagram and a mathematical model for measuring the conversion of vibration displacement into capacitor capacity are proposed. Analytical and graphical dependence of the capacity of the parametric sensor on the displacement of the plates under the action of vibration displacement in the justified range of their possible change from 20 to 120 μm was obtained. It was established that in this range of changes in vibration displacement, the capacity of the capacitor changes within such limits from 3 to 18 nF.

A mathematical model for measuring the transformation of vibration displacement into a time interval was obtained and a graphical dependence of the duration of the time interval τ on the change in the displacement a of the plates under the action of vibration displacement in the set range of movement of the capacitor plates from 20 to 120 μm was given. It is shown that the value of the time constant in this range varies from 100 to 325 μs.

A scheme of a capacitive measuring transducer of vibration displacement in a time interval and time diagrams explaining the principle of its operation are proposed. It is shown that the quantization error will not exceed 0.1 % during further measurement conversion into a binary code. The error from the insensitivity zone of the comparator is of the same order.

The use of such an approach will allow formalizing further research into the measuring channels of vibration monitoring systems of electromechanical systems and complexes.