Анализ чувствительности характеристик поворотно-симметричных многокомпонентных конструкций к варьированию параметров

Abstract

Sensitivity analysis can be used in systems of optimal interactive and automated design, when identifying or updating mathematical models, debugging; non-destructive testing and vibration diagnostics of production and operation, stochastic analysis of characteristics in the field of random deviations of geometric parameters and material properties. In the optimal design of a cyclically symmetric design, taking into account the technological heredity, instead of a deterministic criterion, an evaluation of the functional by the worst or the average statistical deviations of the variable parameters within the limits of tolerances can be considered. The problem of the optimal designation of tolerances at a minimum manufacturing cost with constraints on the worst (within tolerances) deviations of dynamic or strength functionals is considered. The sensitivity analysis of the finite element model allows taking into account the kinematic constraints, the complex geometry of the volumetric form, the distribution of loads and the physical properties of materials. The analysis of the sensitivity of a cyclically symmetrical design is specific in that a complete set of variable parameters is determined by a set describing the design variables of a particular sector. Derivatives of functionals are sought for an entire cyclically symmetric construction. Accounting for cyclic symmetry leads to a significant reduction in the number of arithmetic operations and a significant reduction in the amount of stored and processed information. The methods for analyzing the sensitivity of strength and dynamic characteristics are analyzed. Examples of solving problems for a bearing rolling unit and a reversible hydraulic machine are given.