Prediction Models by Response Surface Methodology for Turning Operation

Basim A. Khidhir; Waleed Al- Oqaiel; PshtwanMuhammed Kareem

doi:10.12691/ajmo-3-1-1

AJMO» Archive» Volume 3» Issue 1»Research Article

OPEN ACCESS Peer Reviewed

PEER-REVIEWED

Prediction Models by Response Surface Methodology for Turning Operation

Basim A. Khidhir^1,, Waleed Al- Oqaiel², PshtwanMuhammed Kareem³

¹Slemani Technical College, Iraq

²Ministry of Industry, Kingdom of Saudi Arabia

³Slemani technical Institute, Iraq

Abstract

1. Introduction

2. Selection of Cutting Data

3. Results and Discussion

4. Conclusions

References

Abstract

This study is intended to develop a predictive model for surface roughness and temperature in turning operation of AISI 1020 mild steel using cemented carbide in a dry condition using the Response Surface Method (RSM). The values of the selected cutting speed, feed rate, and depth of cut are based on the preliminary trial experiments by design of experiments. The analysis of variance for the predictive model of second order for both models shows that the feed rate is the most significant parameter which affects the surface roughness and temperature followed by cutting speed. The goal is to monitor one response by other instead of using different techniques. Both models are convenient for predicting of the main effects of the machining parameters and are economical for determining the influence of various parameters in a systematic manner.

At a glance: Figures

View all figures

123

Prev Next

Keywords: response surface methodology, machining parameters, surface roughness, AISI 1020 mild steel

American Journal of Modeling and Optimization, 2015 3 (1), pp 1-6.
DOI: 10.12691/ajmo-3-1-1

Received November 04, 2014; Revised November 28, 2014; Accepted January 26, 2015

Cite this article:

Khidhir, Basim A., Waleed Al- Oqaiel, and PshtwanMuhammed Kareem. "Prediction Models by Response Surface Methodology for Turning Operation." American Journal of Modeling and Optimization 3.1 (2015): 1-6.

Khidhir, B. A. , Oqaiel, W. A. , & Kareem, P. (2015). Prediction Models by Response Surface Methodology for Turning Operation. American Journal of Modeling and Optimization, 3(1), 1-6.

Khidhir, Basim A., Waleed Al- Oqaiel, and PshtwanMuhammed Kareem. "Prediction Models by Response Surface Methodology for Turning Operation." American Journal of Modeling and Optimization 3, no. 1 (2015): 1-6.

Import into BibTeX

Import into EndNote

Import into RefMan

Import into RefWorks

1. Introduction

The commercial success of a new product is strongly influenced by time factor. Shorter product lead-times are of importance for industry in a competitive market. This can be achieved only if the product development process can be realized in a relatively shorter time frame. However, the development of new cutting inserts involve time consuming trial and error iterations, which mainly due to limited empirical knowledge of the mechanical cutting process [1-6]^[1]. The study of cutting process is further complicated by the fact that material removal occurs in a hostile environment with high temperature and pressure involved in the cutting zone ^{[5, 7]}. A knowledge of these principles makes it possible to model, and thereby to predict the practical results of the cutting process and thus to select optimum cutting conditions for each particular case. One of the well known methods used for studying metal cutting is based on statistical modeling of the machining process to predict surface roughness, temperature and tool wear ^[1]. This model would have a great value in increasing the understanding of the cutting process and in reducing the number of experiments which are traditionally used for tool design, process selection, and machinability evaluation.

The objective of this study is to establish a predictive model that would enable us to predict cutting performance such as cutting temperature, and surface roughness. The ultimate objective of the metal cutting science is to solve practical problems associated with efficient material removal in the metal cutting process. To achieve this, the principles governing the cutting process should be understood.

1.1. Response of Surface Methodology (RSM)

By designing the experiments carefully, the objective of the present study is to optimize a response (output variable) which is influenced by several independent variables(input variables). An experiment is a series of tests, called runs, in which changes are made in the input variables in order to identify the reasons for changes in the output response ^{[8, 9]}. In physical experiments inaccuracy can be due to measurement errors, whereas in computer experiments numerical errors are due to incomplete convergence of iterative processes, round-off errors or the discrete representation of continuous physical phenomena. In RSM, the errors are assumed to be random ^{[8, 9]}. The Response Surface Method (RSM) is a methodology of constructing approximations of the system behavior using results of the response analyses calculated at a series of points in the variable space. Optimization of RSM can be solved according to the following three stages:

1. Design of experiment.

2. Building the model.

3. Solution of minimization problem according to the criterion selected.

Response surface method (RSM) is a combination of experimental, regression analysis and statistical inferences. The concept of a response surface involves a dependent variable y called the response variable and several independent variables x₁, x₂,. . . ,x_k called independent ^{[8, 9]}. If all of these variables are assumed to be measurable, the response surface can be expressed as:

(1)

The goal of the present study is to optimize the response variable y. It is assumed that the independent variables are continuous and controllable by the experimenter with negligible error. The response or the dependent variable is assumed to be a random variable. In a milling operation, it is necessary to find a suitable combination of cutting speed (x₁ = lnV), feed rate (x₂ = lnf), and depth of cut (x₃ = ln d) that optimize response. The observed response y as a function of the speed, feed, depth of cut can be written as ^{[8, 9]}:

(2)

Usually a low order polynomial (first-order and second-order) in some regions of the independent variables is employed. The first-order model is expressed as ^{[8, 9]}:

(3)

and the second –order model ^{[27, 28]},

(4)

for i<j are generally utilized in RSM problems. The β parameters of the polynomials are estimated ^{[8, 9]}.

The RSM is a practical, economical and relatively easy to use and was employed by many researchers for modeling machining processes ^{[10, 11, 12, 13]}. Mead and Pike ^[14] and Hill and Hunter ^[15] reviewed the earliest work on Response Surface Method (RSM). In order to institute an adequate functional relationship between the surface roughness and the cutting parameters (speed, depth of cut and feeds), a large number of tests are required, which in turn require a separate set of tests for each as well as a combination of cutting tool and workpiece material. Fuh and Wu ^[16] proposed a prediction models by using the Takushi method and the Response Surface Method (RSM). By using factors such as cutting speed, feed and depth of cut, Alauddin et al ^[17] developed surface roughness models and determined the cutting conditions for 190 BHN steel and Inconel 718. They found that the variations of both tool angles have important effects on surface roughness. In order to model and analyze the effect of each variable and minimize the cutting tests, surface roughness models which utilize response surface methodology and experimental design were carried out in this investigation. Mishra ^[18] has found out a relationship to study the residual stresses based on a moving heat source under various simulated cutting conditions, but the predicted trend was not in agreement with the results of actual machining. Response Surface Method (RSM) was then utilized for determining the residual stresses under different cutting conditions and for various tensile strengths presented by different materials ^[19]. Wu ^[20] was the first pioneer who used RSM in tool life testing. The number of experiments required to develop a surface roughness equation can be reduced as compared to the traditional one-variable-at-a-time approach. Based on RSM and 23 factorial designs, first- and second-order models have been developed in this project. Only twelve tests were required to develop the first-order model, whereas twenty four tests were needed for the second-order model. Reen ^[21] has pointed out that for accurate rating of machinability, three factors, namely, tool life, surface finish, and power consumed during cutting, must be considered. Similar views were expressed by Shaw ^[22], whereas Taraman ^{[23, 24]} used RSM approach for predicting surface roughness. A family of mathematical models for tool life, surface roughness and cutting forces were developed in terms of cutting speed, feed, and depth of cut. Hasegawa et al., ^[25] conducted 34 factorial designs to conduct experiments for the surface roughness prediction model. They found out that surface roughness increased with an increase in cutting speed. Sundaram and Lambert ^{[26, 27]} considered six variables i.e. speed, feed, depth of cut, time of cut, nose radius and type of tool to monitor surface roughness. Mital and Mehta ^[28] carried out a survey of surface roughness prediction models that influence surface roughness and found out that most of the models were developed for steels. Boothroyd ^[29] and Baradie ^[30] investigated the effect of speed, feed and depth of cut on steel and grey cast iron, and then emphasized the use of RSM in developing a surface roughness prediction model.

2. Selection of Cutting Data

After a preliminary investigation to find the suitable levels of the machining parameters, the researchers used Minitab software to deduce experiments based on Box-Behnken design. The generated levels of independent variables like: cutting speed, feed rate and depth of cut are given in Table 1.

Table 1. The values and levels selected for the variables

Download as

[1]	T.V. SreeramaReddya, T. Sornakumarb, M. VenkataramaReddya, R. Venkatramc, Machinability of C45 steel with deep cryogenic treated tungsten carbide cutting tool inserts, Int. Journal of Refractory Metals & Hard Materials 27 (2009) 181-185.
	In article	CrossRef

[2]	K. V. Sudhakar, J. C. Cisneros, Hector Cervantes and Cosme Gomez Pineda Machining characteristics and fracture morphologies in a copper-beryllium (Cu-2Be) alloy, Journal of Materials Engineering and Performance Volume 15, Number 1, 117-121, (2006).
	In article

[3]	Metal cutting theory and practice by David a. Stephenson and John S.Agapiou, publish by Marcel Dekker, Inc, 1997.
	In article

[4]	Metal Cutting Mechanics by Viktor P. Astakhov, publish by CRC press, 1999.
	In article

[5]	Manufacturing Process and Systems, Ninth Edition; by Philip F. Ostwald and Jairo Munoz, publish by John Wiley & Sons
	In article

[6]	E.M. Trent, Metal Cutting, 3rd ed., Butterworth-Heinemann, 1991.
	In article

[7]	WuyiChen, “Cutting forces and surface finish when machining medium hardness steel using CBN tools”, International Journal of Machine tools and Manufacture, 40 (2000), pp 455-466
	In article

[8]	Design and analysis of Experiments, fifth edition; by Douglas C.Montgomery; publish by John Wiley and Sons
	In article

[9]	Response Surfaces design and analyses second edition; by Andre I.Khuri and John A. Cornell, publish by Marcel Dekker, Inc
	In article

[10]	M. Hasegawa, A. Seireg, R.A. Lindberg, “Surface roughness model for turning”, Tribology International, December (1976), pp 285-289.
	In article

[11]	G.E.P. Box, N.R. Draper, “Empirical model-building and response surfaces”, New York, John Wiley & Sons, (1987).
	In article

[12]	M.A. El Baradie, “Surface roughness model for turning grey cast iron (154BHN)”, Proceeding of Institution of Mechanical Engg, Part B, Journal of Engineering Manufacture, 207 (1993), pp 43-54.
	In article

[13]	R.M. Sundaram, B.K. Lambert,” Mathematical models to predict surface finish in fine turning of steel”, Part I, International Journal of Production Research, 19 (1981), pp 547-556
	In article

[14]	R. Mead, D.J. Pike, “A review of response surface methodology from a biometric viewpoint”, Biometrics, 31 (1975), pp 803-851
	In article

[15]	W. J. Hill, W.G. Hunter,” A review of response surface methodology: a literature survey”, Technometrics, 8 (1966), pp 571-590
	In article

[16]	W.J. Hill, W.G. Hunter, “A review of response surface methodology: a literature survey”, Technometrics, 8 (1966), pp 571-590
	In article

[17]	M. Alauddin, M.A.EL Baradie, M.S.J.Hashmi, “Prediction of tool life in end milling by response surface methodology”, 71(1997), pp 456-465.
	In article

[18]	Mishra, T. Prasad, “Residual stresses due to a moving heat source”, lnt. J. Mech. Sci., 27(9) (1985), pp 571-581.
	In article

[19]	M.E. E1-Khabeery, M. Fattouh,” Residual stress distribution caused by milling”, Int. J. Mach. Tools Manufact., 29 (3) (1989), pp 391 401
	In article

[20]	W. Wu, Y. Matsumoto, “The effect of hardness on residual stresses in orthogonal machining of AISI 4340 steel”, ME J. Eng. Ind., 112 (1990), pp 252.
	In article

[21]	Y. Matsumoto, M.M. Barash, C.R. Liu, “Effect of hardness on the surface integrity of AISI 4340 steel”, SME J. Eng. Ind., 108 (1986), pp 69-175.
	In article

[22]	S.M. Wu, “Tool life testing by response surface methodology”, part i and part ii, Trans. ASME B, 86 (1964), pp 105-116.
	In article

[23]	O.W. Reen,” Modern Developments in Powder Metallurgy”, MPIF Publishers, 10 (1977), pp. 431-451.
	In article

[24]	M.C. Shaw, Metal Cutting Principles, Oxford University Press, New York, 1986.
	In article

[25]	K. Taraman, “Multi machining output ± Multi independent variable research by response surface methodology”, Int. J. Prod. Res, 13 (4) (1975), pp 265-290.
	In article

[26]	M. Hasegawa, A. Seireg, R.A. Lindberg, “Surface roughness model”, Tribology International, 1976, pp 285-289
	In article

[27]	R.M. Sundaram, B.K. Lambert,” Mathematical models to predict surface finish in steel”, Part I, International Journal of Production Research, 19 (1981), pp 547-556.
	In article

[28]	Mital,M. Mehta, “Surface roughness prediction models”, International Journal of Production Research, 26 (1988), pp 1861-1876.
	In article

[29]	G. Boothroyd, Fundamentals of Metal Machining and Machine Tools, McGraw Hill Publishers, 1975.
	In article

[30]	M.A. El Baradie, “Surface roughness model for grey cast iron (154BHN)”, Proceeding of Institution of Mechanical Engg, Part B, Journal of Engineering Manufacture, 207 (1993), pp 43-54.
	In article

Prediction Models by Response Surface Methodology for Turning Operation

Science and Education Publishing

Prediction Models by Response Surface Methodology for Turning Operation

Abstract

At a glance: Figures

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Cite this article:

1. Introduction

2. Selection of Cutting Data

Table 1. The values and levels selected for the variables

Table 2. Design values obtained from the Minitab

3. Results and Discussion

Table 3. Experimental and predicted surface roughness by second order model

Table 4. Estimated regression coefficients for second order predicted surface roughness

Table 5. Analysis of Variance for second order surface roughness model

Table 6. Experiment and prediction result for temperature from second order model

Table 7. Estimated Regression Coefficients for temperature of the second order model

Table 8. Analysis of Variance for second order temperature model

4. Conclusions

References

Pages

Partners

Help & Contacts

Follow Us