International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:06 9 150804-1505-5959-IJMME-IJENS © December 2015 IJENS I J E N S Abstract— The manufacturing process of drilling is considered the most efficient method for opening holes in a variety of materials. The present research aims to study the effects of the drilling parameters such as cutting speed, feed rate and tool diameter used on the prediction of the total thrust force and the thrust force due to the cutting action of the tool’s main cutting edges. The experiments were carried out by varying the drilling parameters and the output responses were mathematically modeled based on the response surface methodology. The analysis of variance was used to verify the adequacy of the mathematical models. The most significant input variables were recognized and the 3D response surfaces were plotted. Index Term— Al7075, drilling, response surface methodology, thrust force. I. INTRODUCTION DRILLING is the most commonly used machining operation in a variety of materials. The quality of the drilled holes is significantly affected by the developed thrust force. A number of researchers have been applying the response surface methodology (RSM) to different manufacturing environments. RSM is a tool for determining the cause and effect relationship between responses and input variables [1]. The basic steps involved can be summarized as follows:  Designing of a set of experiments for adequate and reliable measurement of the response.  Determining the mathematical model with the best fitting.  Finding the optimum set of experimental factors that maximize/minimize the response.  Represent the effects of the variables on the response using 2D or 3D plots. This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund. The paper was submitted in June 2015 P. Kyratsis is with the Technological Education Institute of Western Macedonia, Department of Mechanical Engineering and Industrial Design, Kila Kozani, GR50100, Greece (e-mail: pkyratsis@teiwm.gr). N. Taousanidis is with the Technological Education Institute of Western Macedonia, Department of Mechanical Engineering and Industrial Design, Kila Kozani, GR50100, Greece (e-mail: taousan@teiwm.gr). A. Tsagaris is with the Technological Education Institute of Thessaloniki, Department of Automation Engineering, P.O. Box 141, GR57400, Thessaloniki, Greece (e-mail: tsagaris@autom.teithe.gr) K. Kakoulis is with the Technological Education Institute of Western Macedonia, Department of Mechanical Engineering and Industrial Design, Kila Kozani, GR50100, Greece (e-mail: kkakoulis@teiwm.gr). II. REVIEW OF LITERATURE Onwubolu et al. presented a mathematical model for correlating the interactions of speed, feed rate and drill diameter on the axial force and torque, acting on the cutting tool during drilling. They implemented the response surface methodology with a three-level full factorial design. The results proved that the model can be used for optimization purposes in order to minimize both the axial force and torque [2]. Li et al. drilled a 15mm thick recombinant bamboo and considered the spindle speed, feed rate and diameter for the measurement of both the thrust force and torque. Mathematical models were developed resulting that the main influence on the thrust force came from the spindle speed and feed rate, while for the torque, the diameter of the tool and the spindle speed were the most significant parameters. High spindle speed with low feed rate minimized the thrust force [3]. Krishnaraj et al. investigated the thrust force and surface roughness of plain carbide drill with drill parameters (drill diameter, spindle speed and feed rate) in drilling carbon fibre reinforced plastic (CFRP) laminate/aluminum stack. Taguchi method and the L 27 orthogonal array were used together with the analysis for variance (ANOVA). Feed rate and diameter were the most significant drill parameters. In addition, when the feed increases the circularity increases as well [4]. Prakash and Planikumar studied the use of Taguchi and response surface methodology for predicting the surface roughness in drilling medium density fiberboard (MDF) material by physical vapor deposition TiN coated carbide step drill bits. The drilling parameters used were the spindle speed, feed rate and drill diameter. The effect of these parameters on the surface roughness was evaluated and discussed in details. A second order model was established for calculating the surface roughness from the cutting parameters. Validation experiments were performed in order to examine the accuracy of the proposed models [5, 6]. Sundeep et al. examined the drilling behavior of austenitic stainless steel (AISI316) and optimized the process parameters using L 9 orthogonal array from the Taguchi methodology. Spindle speed, feed rate and drill diameter were used as input parameters, while the lowest thrust force and highest metal Drilling Mathematical Models Using the Response Surface Methodology Panagiotis Kyratsis, Nikolaos Taousanidis, Apostolos Tsagaris, Konstantinos Kakoulis