Multivariate chance-constrained method applied in multi-objective optimization problems of manufacturing processes
| Autor: | TORRES, Alexandre Fonseca |
|---|---|
| Přispěvatelé: | BALESTRASSI, Pedro Paulo, COSTA, Antonio Fernando Branco |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Repositório Institucional da UNIFEI (RIUNIFEI) Universidade Federal de Itajubá (UNIFEI) instacron:UNIFEI |
| Popis: | Agência 1 In the multi-objective optimization problems of manufacturing processes, the responses of interest are often significantly correlated. In addition to the multivariate nature of the problems, product demands, productive capacities, cycle times, the costs of labor, machines, and tools are just some of the many random variables involved in the optimization model. In particular, when using Design of Experiments (DoE) techniques and regression methods, the estimated coefficients for the empirical models - such as response surface models - are also stochastic. However, it has been observed that most of the articles published in this research area are limited to represent the stochastic variables in a deterministic way. Within this context, the present study aimed to propose the use of stochastic programming techniques combined with multivariate statistical methods including some process capability indices widely used in the industry, such as the capacity index and the Parts Per Million () index. The use of the methods combined used resulted in the proposal of the Multivariate Chance-Constrained Programming (MCCP). To test the applicability of the MCCP method, a multi-objective optimization problem of the AISI 52100 hardened steel turning process was selected as a case study given its widespread use and relevance to the industry nowadays. As a starting point for this study, a set of experimental results obtained from a central composite design was used. The decision variables were the cutting speed (), the feed rate () and the depth of cut (). The responses of interest selected for this work were the total machining cost per part (), the material removal rate (), the tool life (), the average roughness () and the total roughness (). After analyzing the data and building the mathematical models for the responses of interest, three approaches were carried out. In the first approach, the index included the calculation of the variance of the response surface model of . In the second approach, the probability that is less than or equal to a predefined value was modelled as a stochastic objective function. Finally, the third approach described the application of the proposed MCCP method. In this approach, the index was calculated using a normal bivariate distribution for both and . The main results of this research were: a) the demonstration and validation of an equation used to calculate the variance of a continuous, derivable and dependent function of stochastic variables; b) the analysis of the impact of seven stochastic industrial variables (setup time, lot size, machine and labor costs, insert changing time, tool holder price, tool holder life and insert price) on the cost of the process; c) finding that maximizing tool life may reduce cost in some cases – for example when using Wiper tools – but the change of the cutting conditions alone does not necessarily reduce the cost of the process, as in what occurred in the case study analyzed. |
| Databáze: | OpenAIRE |
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