Mathematical Problems in Engineering

Volume 2016, Article ID 6749182, 9 pages

http://dx.doi.org/10.1155/2016/6749182

## Modeling of Drilling Forces Based on Twist Drill Point Angles Using Multigene Genetic Programming

^{1}School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China^{2}School of Mechanical Science & Technology, Kimchaek University of Technology, Pyongyang 999093, Democratic People's Republic of Korea

Received 16 October 2015; Accepted 4 January 2016

Academic Editor: Francesco Aymerich

Copyright © 2016 Myong-Il Kim and Ping Zou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The mathematical model was developed for predicting the influence of the drill point angles on the cutting forces in drilling with the twist drills, which was used to optimize those angles for reducing drilling forces. The approach was based on multigene genetic programming, for the training data, the grinding tests of twist drill were firstly conducted for the different drill point angles in Biglide parallel machine, and then drilling tests were performed on carbon fiber reinforced plastics using the grinded drills. The effectiveness of the proposed approach was verified through comparing with published data. It was found that the proposed model agreed well with the experimental data and was useful for improving the performance of twist drill.

#### 1. Introduction

The drilling process is one of the most important and basic metal cutting operations because of its large portion of overall machining operations. Moreover, the drilling problems can result in costly production waste because many drilling operations are usually in the final steps for fabricating a part. In drilling process, the drilling forces are one of the primary responses; therefore, predicting the influences of the drill point geometry on the cutting forces will provide many platforms needed for the evaluation and comparison of new drill designs. The geometry and cutting mechanics of twist drill have been well studied over many years; many models have been developed by many researchers for predicting torque and thrust force in drilling [1–4].

Early drilling models were developed based on the analytical mathematical approach using the mechanics of cutting analysis and the shear plane approach, where the drilling mechanism was analytically described by complicated equations in 3D space; 2D projected geometry was used instead in many cases, in order to reduce the amount of calculation [5, 6]. In these studies, the modeling of drilling process was conducted using a series of oblique cutting slices; after that, it was expanded to the more detailed modeling of material removal in both the cutting lip and chisel edge regions for predicting the drill temperatures and simulating arbitrary drill geometries [7, 8]. More recent developments in drilling models have utilized either a mechanistic or a finite element method. The finite element method was used for determining drilling torque and thrust force and for predicting drill heat flux, temperatures, and the thermal distortion of drill holes based on the Lagrangian and Eulerian methods [3, 9–11]. Chandrasekharan et al. [7, 12] and Hamade et al. [13] developed mechanistic drilling models, where an extensive amount of experiments took place and the results were stored in databases so that different parameters could be used for experimentally derived equations. Mechanistic approach typically involves determining the forces acting along the tool rake face from which the resultant force projected along any desired orientation may be calculated [14–16].

As stated above, although a number of approaches for predicting the drilling forces were developed using the different cutting conditions, there is little research to evaluate the influences of the drill point geometry on the cutting forces.

The drilling forces were found to be mainly dependent on not only the cutting conditions but also the drill point geometry [12, 17]. Moreover, as the point geometry of the twist drill is completely featured with the drill point angles such as the semipoint angle, the chisel edge angle, and the relief angle, the drilling forces depend naturally on the drill point angles. Therefore, it is very significant to formulate the mathematical model of drilling forces in terms of drill point angles for designing a high performance twist drill.

For formulating this model, various advanced mathematical modeling methods could be applied such as support vector regression (SVR), artificial neural network (ANN), and multigene genetic programming (MGGP), which are comprehensively used in engineering problems because of their powerful prediction ability [18, 19]. Amongst these methods, MGGP possesses the ability to evolve the model structure and its coefficients, which shows the advantages in predicting accuracy and reliability compared to the others in many applications [20, 21].

In this paper, the experimental model is presented to predict the influence of twist drill point angles on the cutting forces to be presented based on MGGP method. In order to acquire the training data, the grinding tests and measurements of the drill point angles are conducted on Biglide parallel machine [22] and the drilling tests are performed using carbon fiber reinforced plastics (CFRP) work piece, which is widely used in aerospace industry due to its ability to resist corrosion and withstand high loads while reducing the weight of the structural parts [23–25]. The twist drills with different drill point angles are used in this experiment. The model is verified by comparing predicted drilling force and torque with published data and measured.

#### 2. Preparing of Training Data

In order to prepare the training input data, firstly, the experiments were conducted to grind twenty twist drills with different drill point angles with Biglide parallel machine; the structure is as shown Figure 1 [26].