Mathematical Model of Long-Term Temperature Effects on the Functioning Quality of Electrical Measuring Instruments: Research and Modeling

Abstract

The assessment of long-term stability of electrical measuring instruments (EMI) is a complex task associated with the influence of external factors, where the ambient temperature is the most significant one. Prolonged temperature exposure leads to degradation processes in the electrical, magnetic, and mechanical components of measuring devices (MD), resulting in their accuracy decrease. The main objective of this study is to develop a mathematical model describing the long-term thermal effects on the technical quality of EMI. Unlike the author’s previously proposed model of short-term effects, the present work focuses on the description of irreversible thermal processes. The developed model considers the changes in resistance and temperature coefficient of resistance (TCR), magnetic induction and temperature coefficient of magnetic induction (TCMI), as well as the elasticity and torque of the return spring in analog-pointer (APT) instruments. To describe the dynamics of degradation processes the Arrhenius equation was employed as the basis, enabling the dependency derivation to assess the accuracy parameter variation with time. Simulation results provided accuracy curves for both APT and digital systems. The findings demonstrate that mechanical and magnetic components are more sensitive to thermal effects compared to the electronic parts of digital measuring devices. The proposed model and methodology allow predicting the decline of technical quality of EMI under real operating conditions, accounting for climatic factors when selecting equipment, and adjusting calibration intervals depending on environmental conditions. The practical significance of this work lies in the possibility of integrating the developed tools into quality assessment systems for EMI, thereby improving operational reliability and providing a more objective quantitative evaluation of their condition.