# The Optimization of Machining Parameters for Milling Operations by Using the Nelder Mead Simplex Method

Chien Wern

Fall 1-9-2020

Thesis

## Degree Name

Master of Science (M.S.) in Mechanical Engineering

## Department

Mechanical and Materials Engineering

English

## Subjects

Mathematical optimization, Milling-machines

## DOI

10.15760/etd.7271

## Physical Description

1 online resource (xi, [89] pages)

## Abstract

Machining operations need to be optimized to maximize profit for computer numerical control (CNC) machines. Although minimum production time could mean high productivity, it can not guarantee maximum profit rate in CNC milling operations. The possible range of machining parameters is limited by several constraints, such as maximum machine power, surface finish requirements, and maximum cutting force for the stability of milling operations. Among CNC machining parameters, cutting speed and feed have the greatest effect on machining operations. Therefore, cutting speed and feed are considered as main process variables to maximize the profit rate of CNC milling operations.

A variety of numerical methods are used to optimize the machining process, such as the genetic algorithm, tabu search method, and ant colony algorithm. In CNC milling operations, an objective function proposed by Tolouei and Bidhendi [1996] was used to estimate the profit rate. Tolouei and Bidhendi [1996] used the method of feasible direction to maximize the profit rate of CNC milling processes. In this research, the Nelder-Mead simplex method will be tried to maximize the profit rate of CNC milling processes. The Nelder-Mead simplex method was selected to find an optimum value because it can be used when the derivative of a function is unpredictable due to nonlinearity. As such, this method is suitable for problems of statistical estimation.

Best, worst, and second-worst values are obtained within the simplex algorithm, and it is stopped when its output value goes below stopping criteria. When the Nelder-Mead simplex method was employed, the profit rate achieved was 9.5% higher than the maximum profit rate that is obtained by using the method of feasible direction (Tolouei and Bidhendi [1996]).

## Rights

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## Persistent Identifier

https://archives.pdx.edu/ds/psu/31000

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