successive calculation
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Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2116
Author(s):  
Miguel A. Sainz ◽  
Remei Calm ◽  
Lambert Jorba ◽  
Ivan Contreras ◽  
Josep Vehi

The system of marks created by Dr. Ernest Gardenyes and Dr. Lambert Jorba was first published as a doctoral thesis in 2003 and then as a chapter in the book Modal Interval Analysis in 2014. Marks are presented as a tool to deal with uncertainties in physical quantities from measurements or calculations. When working with iterative processes, the slow convergence or the high number of simulation steps means that measurement errors and successive calculation errors can lead to a lack of significance in the results. In the system of marks, the validity of any computation results is explicit in their calculation. Thus, the mark acts as a safeguard, warning of such situations. Despite the obvious contribution that marks can make in the simulation, identification, and control of dynamical systems, some improvements are necessary for their practical application. This paper aims to present these improvements. In particular, a new, more efficient characterization of the difference operator and a new implementation of the marks library is presented. Examples in dynamical systems simulation, fault detection and control are also included to exemplify the practical use of the marks.


2021 ◽  
Vol 64 (5) ◽  
pp. 353-359
Author(s):  
A. S. Vusikhis ◽  
L. I. Leont’ev ◽  
E. N. Selivanov

To predict the conditions for metals reduction from an oxide melt by gas in bubbling processes, a thermodynamic modeling technique has been developed that provides an approximation to real systems. The main difference between the accepted method and the well-known one is in conducting successive calculation cycles with withdrawal of the generated gases and the metal phase from the working medium. This paper presents the results of thermodynamic modeling of nickel and iron reduction processes from B2O3 – CaO– Fe2O3 – NiO melts by mixtures of CO– CO2 and H2 – H2O containing 0 – 60 % CO2 (H2O) in the temperature range of 1273 – 1673 K. The calculations evaluated the content of nickel and iron oxides in the melt and the degree of their reduction. It is shown that, regardless of the gas composition, this process proceeds in several stages. At the first stage, Fe2O3 is reduced to Fe3O4 and FeO. СFe2O3 values decrease to almost zero, while СFe3O4 and CFeO increase simultaneously. By the end of the phase, СFeO reaches its maximum value. At the second stage, the Fe3O4 → FeO transition occurs, when СFe3O4 values reach maximum, nickel and iron begin to reduce to metal. At reduction by CO– CO2 mixture, an increase in temperature reduces the metallization of both nickel and iron. Similarly, an increase in the CO2 content of the introduced gas affects. During interaction of the oxide melt with a gas containing 60 % CO2 , the third stage is absent. At reduction by H2 – H2O mixture, an increase in temperature reduces the metallization of nickel, but increases metallization of iron. With increasing water vapor content in the introduced gas, the degree of metallization of both nickel and iron decreases. The obtained data are useful for creating technologies for selective reduction of metals and formation of ferronickel of the required composition.


2016 ◽  
Vol 36 (3) ◽  
pp. 295-307 ◽  
Author(s):  
Zhengping Chang ◽  
Zhongqi Wang ◽  
Bo Jiang ◽  
Jinming Zhang ◽  
Feiyan Guo ◽  
...  

Purpose Riveting deformation is inevitable because of local relatively large material flows and typical compliant parts assembly, which affect the final product dimensional quality and fatigue durability. However, traditional approaches are concentrated on elastic assembly variation simulation and do not consider the impact of local plastic deformation. This paper aims to present a successive calculation model to study the riveting deformation where local deformation is taken into consideration. Design/methodology/approach Based on the material constitutive model and friction coefficient obtained by experiments, an accurate three-dimensional finite element model was built primarily using ABAQUS and was verified by experiments. A successive calculation model of predicting riveting deformation was implemented by the Python and Matlab and was solved by the ABAQUS. Finally, three configuration experiments were conducted to evaluate the effectiveness of the model. Findings The model predicting results, obtained from two simple coupons and a wing panel, showed that it was a good compliant with the experimental results, and the riveting sequences had a significant effect on the distribution and magnitude of deformation. Practical implications The proposed model of predicting the deformation from riveting process was available in the early design stages, and some efficient suggestions for controlling deformation could be obtained. Originality/value A new predicting model of thin-walled sheet metal parts riveting deformation was presented to help the engineers to predict and control the assembly deformation more exactly.


2014 ◽  
Vol 655 ◽  
pp. 15-20 ◽  
Author(s):  
Sven Kreitlein ◽  
Tobias Rackow ◽  
Jörg Franke

This paper introduces a method for the assessment and evaluation of energy efficiency of the manufacturing processes in the production as well as a corporate and cross-industry comparison. Already today, energy-related characteristic value systems are used, which are related to the energy consumption of large electronic household appliances or are focusing on their production facilities. The energy efficiency value is a newly developed indicator and will provide valuable information about the energy efficiency of the production of various products, production operators, and consumers. In the following, the energy efficiency value, which is based on the approach of minimal value calculation, is presented in detail. The basic idea is the comparison and evaluation of energy efficiency based on the ratio of the theoretically required energy consumption to the actual energy consumption. Depending on the analysis of influencing factors, a model highlighting their dependencies could be established. The developed system hinges on a successive calculation of the minimum value. Each of these minimum types can be put in relation to the measured energy consumption. However, depending on the chosen basis, the conclusion and focus of the calculated key figure may vary. By using the real minimum as a basis, the actually existing energy savings become visible. The method will be put to the test through an exemplary application for processes in the fields of cutting technologies. This course of action allows for the validation of the developed energy efficiency value and reveals the potential of this method.


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