Physical and mathematical model of optimal geometric dimensions of a strain gauge for a dual-diaphragm pressure sensor based on numerical modeling

The study is devoted to solving an urgent scientific and applied problem of improving the metrological characteristics of strain gauge pressure sensors, in particular, their sensitivity in the field of low pressure measurement. The relevance of the work is due to the fact that in modern instrumentation there remains a need to miniaturize and improve the accuracy of measuring transducers, while the issue of purposeful optimization of the geometry and location of strain-sensitive elements often remains insufficiently studied. The main goal is to determine the optimal combination of the load cell size and its placement relative to the membrane to increase the output signal level in the field of low pressure measurement. To achieve this goal, detailed three-dimensional modeling using the finite element method was carried out in a specialized engineering software package. The use of a complete spatial model made it possible to analyze with high reliability the distribution of deformations in the complex composite structure of the sensor and to assess the influence of variations in geometry. Based on an extensive numerical experiment, by systematically varying the parameters, general patterns of changes in the mechanical response were identified. The obtained data set served as the basis for constructing a generalized physicomathematical model of the relationship between the geometry of the sensor element and the resulting strain difference. The model developed using regression analysis methods has a separate view for different zones of the element location, which increases its adequacy. The main scientific result is the developed model, which makes it possible to evaluate and rationally select the geometric configuration of the load cell at the design stage. The practical significance of the work lies in the formulation of specific recommendations for choosing the optimal proportions and location of the sensing elements to achieve the maximum output signal level. The results are of value to engineers and researchers involved in the development and optimization of highly sensitive measuring equipment in fields such as aerospace engineering, energy, robotics, and industrial automation.

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