Уточнений розрахунок на міцність захисних оболонок термоперетворювачів за умов експлуатації

Abstract

Запропоновано наближений метод порядкових статистик для опрацювання випадкових спостережень за апріорі невідомого розподілу ймовірності генеральної сукупності. Використання наближеного методу не потребує складних розрахунків інтегралів і коваріаційна матриця визначається за допомогою простих арифметичних операції. Подано результати наближеного методу і продемонстровано його ефективність. Разработана численная методика исследования процессов деформирования защитных оболочек термопреобразователей в условиях сложного силового и температурного нагружения на основе трехмерных соотношений термомеханики. Выполнены исследования защитных оболочек различных типоразмеров на статическую и циклическую прочность в условиях их гидравлических испытаний эксплуатации и установлены коэффициенты их запаса. Accurate evaluation of possible safe operation of thermowells essentially depends on the accuracy of the maximum stresses in them during operation. These stresses are generally determined from simple engineering formulas for bulk of canonical shape, mostly cylindrical shells or beams for the relevant boundary conditions. Thus the general solution is obtained step by step. First the tangential stresses are obtained from relations for cylinder subjected to external pressure. Next, axial stress is estimated and the stability of the thermowell is researched from the equations for cylindrical rod. The additional bending stresses that occur during flow of working environment (fluid or steam) around the thermowell, determined on the basis of simple ratios of strength ofmaterials, considering cylindrical beam set perpendicular to the direction of the flow; the beam is clamped at one end and is free at the other one. Then the resulting maximum stress, obtained as a sum of these categories of stresses, is compared with the stress, admissible for material. The possible error of this approach is compensated by introducing a safety factor. However, in general, the thermowells are the spatial solids with complex geometric shapes, and their stress-strength state is spatially non-uniform during operation. So determination of stresses in them using simple engineering formulas, obtained for simplest elements of mechanical systems, can lead to significant errors. This article deals with the problem of estimation of resource and operational reliability of thermowells. In the proposed approach the thermowells are considered as a three-dimensional solids, and the computer simulation of deformation processes in thermowells under operational conditions is executed on the basis of refined spatial three-dimensional models of stress calculation in solids under complex force and temperature loading. Numerical analysis of thermowell stress-strength state is performed using the finite element method. It allows to describe adequately complex geometric shape and three dimensional stress-strength state of thermowell during its operation, and to identify the most loaded areas of thermowell. This approach also allows us to estimate the limits of applicability of simple engeneer formulas, which are used as a rule in the practice of thermowells strength estimation. The strength calculations of the thermowells of different sizes made from a steel 08H18N10T and types during hydraulic test (at pressure 36 MPa) and operation conditions (at pressure 25 MPa, temperature 365 °C, for different velocities of water and water vapor – from 0 to 120 m/s) are fulfilled, and their safety factors are determined on the basis of the proposed approach. In particular, the safety factor for the most loaded thermowell is about 1,4 (compared maximum of stress intensity in the thermowell with a yield stress of the steel at operating temperature) and 3 (in comparison with the tensile strength). Whereas, steel 08H18N10T can significantly strengthen during the plastic deformation, the actual safety factors are larger than calculated ones. The research of convergence obtained numerical solutions is fulfilled. The results of comparative analysis of the solutions based on the proposed approach and standardized methods using simple engineering relationships are shown. In particular, the maximal stress intensities inmost loaded thermowell during operational conditions obtained from these two approaches differ in 1.5 times. So the use of simple engineering formulas in this case leads to higher values ofmaximal stresses. The analysis of a cyclic fatigue calculation shows that the possibility of destruction of thermowells caused by low cycle fatigue during operation is unlikely (we get over 33,000 acceptable cycles “initial state – operational mode – initial state” or “loading – unloading” for the most loaded thermowell during operation). The proposed approach can be used for determining the geometry of thermowell at the fixed conditions of operation and for determining the parameters of operation modes (for example, the pressure or velocity of working environment, etc.) for specific parameters of thermowell fixed geometry.