## 1. Introduction

Roughness plays an important role in determining how a real object will interact with its environment. Rough surfaces usually wear more quickly and have higher friction coefficients than smooth surfaces. Roughness is performance of a mechanical component, since irregularities in the surface may form nucleation soften a good prediction for cracks or corrosion. Although roughness is usually undesirable, it is difficult and expensive to control in manufacturing. Decreasing the roughness of a surface will usually exponentially increase its manufacturing costs. This often results in a trade-off between the manufacturing cost of a component and its performance in an application.

Planning of experiments through design of experiments has been used quite successfully in process optimization by Chen and Chen [

1], Fung and Kang [

2], Tang

et al. [

3], Vijian and Arunachalam [

4], Yang [

5] as well as Zhang

et al. [

6],

etc. Four controlling factors including the cutting speed, the feed rate, the depth of cut, and the cutting fluid mixture ratios with three levels for each factor were selected. The Grey relational analysis is then applied to examine how the turning operation factors influence the quality targets of roughness average, roughness maximum and roundness. An optimal parameter combination was then obtained. Additionally, ANOVA was also utilized to examine the most significant factors for the turning process when the roughness average, roughness maximum and roundness are simultaneously considered.

Aslan

et al., [

7], using Design optimization of cutting parameters when turning hardened AISI 4140 steel (63 HRC) with Al

_{2}O

_{3} + TiCN mixed ceramic tool used an orthogonal array and the analysis of variance (ANOVA) to optimization of cutting parameters. The flank wear (VB) and surface roughness (Ra) had investigated. Nalbant

et al. [

8] used a Taguchi method to find the optimal cutting parameters for surface roughness in turning operations of AISI 1030 steel bars using TiN coated tools. Three cutting parameters, namely, insert radius, feed rate, and depth of cut, are optimized with considerations of surface roughness, and so on. However, very few studies have been conducted to investigate roundness under different turning parameters. Additionally, proper application of cutting fluids as studied by Kalpakjian and Schmid, [

9] and EI Baradie, [

10], can increase productivity and reduce costs by allowing one to choose higher cutting speeds, higher feed rates and greater depths of cut. Effective application of cutting fluids can also increase tool life, decrease surface roughness, increase dimensional accuracy and decrease the amount of power consumed. Water-soluble (water-miscible) cutting fluids are primarily used for high speed machining operations because they have better cooling capabilities [

10]. There fluids are also best for cooling machined parts to minimize thermal distortions. Water-soluble cutting fluids are mixed with water at different ratios depending on the machining operation. Therefore, the effect of water-soluble cutting fluids under different ratios was also considered in this study.

A recent investigation performed by Alauddin

et al. [

11] has revealed that when the cutting speed is increased, productivity can be maximised and, meanwhile, surface quality can be improved. According to Hasegawa

et al. [

12], surface finish can be characterised by various parameters such as average roughness (Ra), smoothening depth (Rp), root mean square (Rq) and maximum peak-to-valley height (Rt). The present study uses average roughness (Ra) for the characterisation of surface finish, since it is widely used in industry. By using factors such as cutting speed, feed rate and depth of cut, Hashmi and his coworkers [

13,

14] have developed surface roughness models and determined the cutting conditions for 190 BHN steel and Inconel 718. EI-Baradie [

15] and Bandyopadhyay [

16] have shown that by increasing the cutting speed, the productivity can be maximised and, at the same time, the surface quality can be improved. According to Gorlenko [

17] and Thomas [

18], surface finish can be characterised by various parameters. Numerous roughness height parameters such as average roughness (Ra), can be closely correlated. Mital and Mehta [

19] have conducted a survey of the previously developed surface roughness prediction models and factors influencing the surface roughness. They have found that most of the surface roughness prediction models have been developed for steels.

## 4. Results and Discussion

After conducting the first pass (one pass is equal to 90 mm length) of the 27 cutting experiments, the surface roughness readings are used to find the parameters appearing in the postulated first order model (

Equation 1). In order to calculate these parameters, the least squares method is used with the aid of Minitab. The first-order linear equation used to predict the surface roughness is expressed by

Equation 7:

where the

C_{speed},

f,

a_{depth} and

r_{depth} are the cutting speed, feed rate, axial depth and radial depth respectively.

Generally, reduction of cutting speed, axial depth of cut caused a larger surface roughness. On the other hand, the increase in feed rate and radial depth caused a slight reduction of surface roughness. The feed rate is the most dominant factor on the surface roughness, followed by the axial depth, cutting speed and radial depth, respectively. Hence, a better surface roughness is obtained with the combination of low cutting speed and axial depth, high feed rate and radial depth. Similar to the first-order model, by examining the coefficients of the second-order terms, the feedrate (

f) has the most dominant effect on the surface roughness. After examining the experimental data, it can be seen that the contribution of cutting speed (

C_{speed}) is the least significant. As seen from

Figure 2, the predicted surface roughness using the second order RSM model is closely matched with the experimental results. It exhibits better agreement compared to those from the first-order RSM model. A contour plot of feed rate

versus cutting speed for the first-order model is shown in

Figure 3. It is clear that the relationship between the surface roughness and design variables can be obtained. The analysis of variance (ANOVA) for first order is tabulated in

Table 4. It indicates that the model is adequate as the

P-value of the lack-of-fit is not significant (>0.05).