Susmita Roy

Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

The numerical algorithm for solving “first-order linear differential equation in fuzzy environment” is discussed. A scheme, namely, “Runge-Kutta-Fehlberg method,” is described in detail for solving the said differential equation. The numerical solutions are compared with (i)-gH and (ii)-gH differential (exact solutions concepts) system. The method is also followed by complete error analysis. The method is illustrated by solving an example and an application.

Multiobjective optimization of in situ process parameters in preparation of Al-4.5%Cu–TiC MMC using a grey relation based teaching–learning-based optimization algorithm

In modern in situ composite fabrication processes, the selection of optimal process parameters is greatly important for the preparation of best quality metal matrix composite. For achieving high-quality composite, an efficient optimization technique is essential. The present study explores the potential of a new robust algorithm named teaching–learning-based optimization algorithm for in situ process parameter optimization problems in fabrication of Al-4.5%Cu–TiC metal matrix composite fabricated by stir casting technique. Optimization process is carried out for optimizing the in situ processing parameters i.e. pouring temperature, stirring speed, reaction time for achieving better mechanical properties, i.e. better microhardness, toughness, and ultimate tensile strength. Taguchi’s L25 orthogonal array design of experiment was used for performing the experiments. Grey relational analysis is used for the conversion of the multiobjective function into a single objective function, which is being used as the objective function in the teaching–learning-based optimization algorithm. Confirmation test results show that the developed teaching–learning-based optimization model is a very efficient and robust approach for engineering materials process parameter optimization problems.

Application of fuzzy technique for order preference by similarity to ideal solution in computer numerical control end milling of in-situ Al-4.5%Cu-TiC metal matrix composite

In the present investigation, an effort has been made to explore the outcome of cutting parameters (cutting speed, feed and depth of cut) on surface roughness parameters (Ra, Rz) and cutting force (Fc) using solid carbide end mill cutter. During the existing study, a novel fuzzy technique for order preference by similarity to ideal solution, grey relational and response surface analysis technique is utilized to find out the optimal settings of computer numerical control milling process parameters with an endeavour to improve the quality of the machined surface. Hence, generating optimum surface roughness values are essential to obtain high productivity in the manufacturing of different machined parts. In this article, the first motive is to investigate computer numerical control milling of Al-4.5%Cu-TiC metal matrix composite developed by in-situ technique using fuzzy technique for order preference by similarity to ideal solution and grey relational analysis to find out optimum cutting parameters. The second motive is to verify using response surface analysis mathematical model depending on cutting parameters of surface roughness and cutting force in milling. The potentiality of the developed model is proved by analysis of variance technique. The analysis of variance result shows that the depth of cut is the leading process parameter affecting the surface roughness and cutting force values.