International Journal of Engineering Advanced Research eISSN: 2710-7167 | Vol. 5 No. 2 [June 2023]
Journal website: http://myjms.mohe.gov.my/index.php/ijear
SURFACE ROUGHNESS ANALYSIS OF HOT TURNING AISI 4340 USING THE RESPONSE SURFACE
METHODOLOGY
Cindy Hartita1* and Irsyadi Yani2
1 2 Master Program of Mechanical Engineering, Faculty of Engineering, Universitas Sriwijaya, South Sumatera, INDONESIA
*Corresponding author: [email protected]
Article Information:
Article history:
Received date : 18 April 2023 Revised date : 2 May 2023 Accepted date : 23 May 2023 Published date : 6 June 2023
To cite this document:
Hartita, C., & Yani, I. (2023).
SURFACE ROUGHNESS ANALYSIS OF HOT TURNING AISI 4340 USING THE RESPONSE SURFACE METHODOLOGY.International Journal of Engineering Advanced Research, 5(2), 48-60.
Abstract: To achieve a high quality of surface, it would be thoughtful to apply environmentally friendly machining processes (green machining). For lathe machining, the hot turning method on the workpiece is a good choice as it is simple to operate and does not require the use of coolants, making it environmentally friendly. The aim of this study was to evaluate the machining performance of AISI 4340 on the dependent variable (surface roughness (Ra) and tooltip temperature). Modelling predictions and optimization are determined using the Response Surface Methodology (RSM). The CCD (Central Composite Design) method is used to determine the variation in the value of the independent variables (cutting speed (Vc), feed rate (fz), depth of cut a and workpiece temperature (Tw)) with a total of 30 test data. The best result of the mathematical equation based on RSM for predicting surface roughness using coated tools is a quadratic model. Surface roughness is most affected by the feed rate of 22%
followed by the depth of cut of 5%. Cutting speed and workpiece temperature by 3%. Therefore, reducing the feed rate can result in better surface roughness. The optimum value in this study is the lowest heat flux value for each cutting speed and constant feed motion, at a depth of cut of 0.5 mm.
Keywords: AISI 4340, Flame Torch, RSM, Heat Conduction.
1. Introduction
Sustainable manufacturing processes that employee different machining condition, such as dry machining, Minimum Quantity Lubrication (MQL), and cryogenic machining (Kok, Amin, and Ismail 2005). MQL uses a minimal amount of lubricant, while cryogenic machining does not use any lubricant. This techniques have been to lower production, reduce environmental impact, and eliminate health hazards for workers (Rahim et al. 2016).
To improve the machinability of high-strength materials, heating the workpiece before or during machining has been identified as an effective solution. This reduces the shear strength of the workpiece, making it easier to work on, and reducing cutting forces and tool wear. Response surface methodology (RSM) and face-cantered composite design (CCD) have been used to model the effect of temperature on flank wear and surface roughness. The results show an optimal temperature range where tool wear is minimized. However, this hot machining technique is not suitable for turning operations due to the design of the coil, which obstructs the last part of the workpiece. Despite attempts to customize the coil design, it is not universally recommended for all turning operations. Induction heat-assisted machining is a promising alternative for vertical milling operations of difficult-to-cut metals and alloys. However, further research is needed to make it more suitable for turning operations (Kumar Parida & Maity, 2019;
Nurul Amin & Ginta, 2014).
Hot machining is a significant alternative for turning operations on difficult-to-cut materials like ceramics, superalloys, and titanium alloys. These materials have high mechanical properties and low thermal conductivity, leading to excessive cutting forces and temperatures during the machining process, which can reduce the lifespan of the tool (Özler, Inan, and Özel 2001). The HUAT technique is shown to effectively decrease cutting forces and stress but results in higher cutting temperatures compared to conventional and ultrasonic-assisted turning methods.
Another method of machining hard to cut materials is heat-assisted machining, which uses an external heat source to reduce material hardness by decreasing bonding energy and yield strength. The hot machining method is one of the important alternatives used to perform metal turning processes on materials that are difficult to cut such as superalloys, titanium alloys and ceramics. The material has high mechanical properties and low thermal conductivity. This can cause excessive cutting forces and cutting temperatures during the machining process and can reduce the life of the tool blade. It is confirmed that HUAT technique reduces cutting forces and effective stress significantly, but cutting temperature increases compared to conventional and ultrasonic assisted turning. Heat-assisted machining is another method to machine hard-to-cut materials using an external heat source. This method allows the material to reduce the hardness by decreasing the bonding energy and yield strength (Sofuoglu et al. 2018).
The surface roughness of a workpiece is an important parameter in the machining process, in addition to temperature and tool wear. The main effects plot shows that cutting speed and feed have a greater impact on cutting temperature than the depth of cut. The Response Surface Method (RSM) was used to optimize cutting temperature, which is a powerful and unique optimization procedure. Increasing cutting speed, feed, and depth of cut all lead to higher cutting temperatures, with a sharp increase in temperature when feed and cutting speed are elevated.
However, the effect of the depth of cut on the cutting temperature is not very significant (Sahoo and Mishra 2014). Rudrapati et al. (2016) have all used RSM to optimize process parameters for different materials and desired outcomes, showing the effectiveness of this approach. The RSM model has better prediction capabilities compared to the ANN model for this experiment,
as evidenced by a lower MAPE value. Excessive heat can cause surface roughness on the workpiece, leading to undesired turning results.
The application of modelling techniques can increase the effectiveness of machining operations and reduce production time and costs, which would benefit the manufacturing industry.
However, analytical models used in machining operations are often nonlinear and may require simplifications and assumptions, which can lead to less accurate results. Therefore, researchers have turned to Response Surface Methodology (RSM) and Artificial Intelligence (AI) models to develop nearly optimal conditions in metal machining. The RSM and AI approaches have been successfully used in many studies and are recommended for real-time applications. In this research, surface roughness (Ra) was considered as the performance parameter for monitoring surface texture, and the ANN approach was used to predict surface roughness during the hard turning of H13 tool steel with the minimal cutting fluid application (Anuja Beatrice et al. 2014).
The Response Surface Methodology (RSM) is a set of mathematical and statistical techniques that are employed for designing, improving, and optimizing experiments. RSM is a valuable tool for studying the interactions between different variables and for optimizing responses with a minimal amount of experimental data. The objective of RSM is to establish a model that optimizes the relationship between one or more independent variables and a response variable of interest (Raymond, Douglas C., and Christine M. 2009). This methodology is commonly used in both scientific and industrial research to improve product or process design, reduce costs, and enhance efficiency. In most real-world applications, RSM is used to measure multiple responses to a product or process (Raymond et al. 2009).
The Response Surface Methodology (RSM) relies on regression analysis principles and employs a group of mathematical equations to develop a model of the response variable as a function of the independent variables. These equations are often polynomial functions that are fitted to the data utilizing regression methods. The resulting model can be utilized to forecast the response variable for any set of values of the independent variables
Generally, the RSM process involves three stages. Initially, a physical experiment is conducted by varying the experimental parameters to obtain reactive values. This method allows for a smaller number of experiments to be performed compared to traditional methods, resulting in reduced costs. Based on the analysis of the results obtained, a mathematical model is developed that can quickly predict the value of an unknown intermediate reaction. In the second stage, the input parameters of the reactions are defined as either second-degree polynomial functions or exponential functions. In the final stage, the optimum point is predicted using analyses such as surface graphs and ANOVA. In this research, the variance analysis (ANOVA) was used to determine the critical states of the cutting parameters, while the optimization of the parameters affecting surface roughness was achieved using the Response Surface Methodology (RSM), which is based on the Taguchi orthogonal test design (Asiltürk, Neşeli, and Ince 2016).
RSM is advantageous compared to other experimental design techniques, since it is efficiently determining the optimal values of independent variables, even in situations where the relationship between variables and the response is intricate. It can also estimate the uncertainty related to the forecasted response variable, that is critical in evaluating the model's reliability.
The RSM technique has some limitations despite its advantages. It can only be used in situations where the relationship between the independent and response variables is smooth, and continuous. It may not work in cases where there is high nonlinearity or discontinuity in the relationships. Furthermore, using RSM requires a significant number of experiments, which can be costly and time-consuming.
2. Literature Review
The Response Surface Methodology (RSM) describes mathematical models to illustrate the association between the response variable and input variables. The models can be categorized as linear, quadratic, or higher-order models, depending on the complexity of the system being investigated.
A quadratic RSM model can be expressed mathematically in a general form as:
𝑦 = 𝛽0+ 𝛽1𝑥1+ 𝛽2𝑥2+ ⋯ + 𝜀 Second order model:
𝑦 = 𝛽0+ ∑ 𝛽𝑖𝑥𝑖
𝑘
𝑖=1
+ ∑ 𝛽𝑖𝑖
𝑘
𝑖=1
𝑥𝑖2+ ∑ 𝛽𝑖𝑗𝑥𝑖𝑥𝑗
𝑘
𝑖 < 𝑗
+ 𝜀
Figure 1: Flow Chart of the Research Start
Experimental Design
Surface Roughness
Responses Surface Methodology
ANOVA
Model Validation
The Best Equation
Finish
NO
YES
This research considered several independent variables, including cutting speed (𝑉𝑐), feed rate (𝑓), depth of cut (𝑎), and workpiece temperature (𝑇𝑤). To reduce the amount of data collected, they utilized a central composite design, which includes factorial points, centre points, and axial points. The factorial points were coded with level -1 and level +1, while the centre points were given a code of 0. The axial points were located between the factorial and centre points. The experiment planning with this design aimed to obtain maximum-quality results
In this research, a quadratic model was used to examine the relationship between the response variable and input variables. The model involved regression constants 𝛽0 , 𝛽𝑖, 𝛽𝑗 , and input variables 𝑥𝑛, 𝑥𝑖, 𝑥𝑗 in a linear equation, with the response variable (y) and error term (ε). Analysis of the equation was based on ANOVA. The model assumed that the relationship between the response variable and input variables was quadratic, with interactions between the input variables taken into account (Bartarya and Choudhury 2012). This research aimed to investigate the nature of this relationship between response and input variables.
In the field of manufacturing, the Response Surface Methodology (RSM) is often used to optimize the production process and improve product quality. To apply RSM, a set of experiments is conducted with different levels of input variables such as temperature, pressure, and flow rate. The response variable, such as the yield or quality of the product, is measured for each experiment.
Using regression analysis, the values of the coefficients 𝛽0 , 𝛽𝑖, and 𝛽𝑗 are estimated, which provide insights into the effect of each input variable on the response variable. Once the model is fitted, it can be used to predict the response variable for new input values within the range of the original experiments. Additionally, the model can be used to find the optimal values of the input variables that maximize the response variable while adhering to process constraints.
By applying RSM, manufacturers can improve their production processes, reduce waste and improve product quality, leading to increased efficiency and profitability.
3. Result and Discussion
The statistical analysis of the linear surface roughness of AISI 4340 using the hot machining method is presented in Table 1. The ANOVA results indicate that the model is significant, as evidenced by an F-Value of 3.87 and a P-Value of 0.0139. A P-Value less than 0.05 is considered significant, whereas a P-Value greater than 0.1000 suggests that the model is not significant. The Lack of Fit F-value of 2.73 is not significant, which is a desirable outcome indicating good modelling. This means that the response data is consistent with the model.
Table 1: ANOVA Surface Roughness Linear Modelling AISI 4340 Source Sum of
Squares DoF Mean
Square F-Value P-Value
Model 0.9719 4 0.2430 3.87 0.0139 Significant
A-Vc 0.0169 1 0.0169 0.2689 0.6086
B-f 0.9033 1 0.9033 14.40 0.0008
C-a 0.0401 1 0.0401 0.6396 0.4314
D-T 0.0116 1 0.0116 0.1845 0.6712
Residual 1.57 25 0.0627
Lack of Fit 1.44 20 0.0718 2.73 0.1348
Not Significant Pure Error 0.1318 5 0.0264
Cor Total 2.54 29
The surface roughness of AISI 4340 during lathe machining with the hot machining method was modelled using response surface methodology, and the results of the linear analysis are presented in the empirical equation below:
y = 1.02 − 0.0306𝑥1+ 0.2240𝑥2+ 0.0472𝑥3− 0.0254𝑥4
The surface roughness (y) in this research was influenced by four independent variables, including cutting speed (𝑥1), feed rate (𝑥2), depth of cut (𝑥3), and workpiece temperature (𝑥4).
Equation 3 of the linear model showed that the cutting speed, feed rate, depth of cut, and workpiece temperature affected the surface roughness by 3.06%, 22.40%, 4.72%, and 2.54%, respectively. The result indicated that feed rate was the most significant variable that influenced the increase in surface roughness, accounting for 22.40%. Previous studies have also described similar results, with Patel & Patel (2012) highlighting the significant impact of feed rate on surface roughness, Ranganathan et al. (2010) emphasizing the effect of cutting speed on power consumption, and Yanis et al. (2019) showing that feed rate had a more significant effect than axial depth of cut. Additionally, this research revealed that the depth of cut was the least significant parameter in predicting the surface roughness of the machined surface. Overall, the results suggest that feed rate plays a critical role in determining surface roughness, with a coefficient value greater than cutting speed, depth of cut, and temperature.
According to equation 3, it can be inferred that the surface roughness of the workpiece subjected to lathe machining using the hot turning method becomes better as the temperature of the workpiece increases. Conversely, an increase in the cutting speed, in feed rate, and depth of cut lead to lower quality surface roughness of the workpiece. Equation 4 represents a linear equation based on the actual factors:
𝑅𝑎 = 0.783110 − 0.001225𝑉𝑐 + 4.26709𝑓 + 0.094433𝑎 − 0.000507𝑇𝑤
The results of the analysis of variance (ANOVA) for modelling the surface roughness quadratic lathe machining AISI 4340 with the hot machining method are presented in Table 2. The ANOVA revealed that the model was significant, as evidenced by a P-Value of 0.0084 and an F-Value of 3.70. A P-Value less than 0.05 is typically used to indicate that the model is significant, while a P-Value greater than 0.1000 suggests that the model is not significant. The Lack of Fit was not significant, indicating that the model was a good fit for the response data,
with an F-Value of 1.66. Overall, the results suggest that the quadratic lathe machining of AISI 4340 using the hot machining method can be successfully modelled to predict surface roughness, with a good fit between the model and the response data.
Table 2: Surface Roughness Quadratic Modelling Using ANOVA for AISI 4340 Source Sum of
Squares DoF Mean
Square F-Value P-Value
Model 1.97 14 0.1407 3.70 0.0084 Significant
A-Vc 0.0169 1 0.0169 0.4440 0.5153
B-f 0.9033 1 0.9033 23.77 0.0002
C-a 0.0401 1 0.0401 1.06 0.3204
D-T 0.0116 1 0.0116 0.3046 0.5891
AB 0.0994 1 0.0994 2.62 0.1267
AC 0.0101 1 0.0101 0.2646 0.6145
AD 0.1536 1 0.1536 4.04 0.0627
BC 0.0060 1 0.0060 0.1581 0.6965
BD 0.1132 1 0.1132 2.98 0.1049
CD 0.0303 1 0.0303 0.7983 0.3857
𝐴2 0.2159 1 0.2159 5.68 0.0308
𝐵2 0.0034 1 0.0034 0.0896 0.7687
𝐶2 0.0745 1 0.0745 1.96 0.1817
𝐷2 0.0667 1 0.0667 1.75 0.2052
Residual 0.5700 15 0.0380
Lack of Fit 0.4383 10 0.0438 1.66 0.2992 Not
Significant
Pure Error 0.1318 5 0.0264
Cor Total 2.54 29
The empirical equation obtained from the quadratic analysis of the surface roughness of AISI 4340 lathe machining with the hot machining method using response surface methodology is presented in this research. The equation can be used to predict the surface roughness of the machined material based on the independent variables considered in the research. The equation is typically in the form of a second-order polynomial and contains the coefficients for the independent variables, as well as interaction terms between them. The coefficients can be estimated using regression analysis of the experimental data. In this research, the empirical equation for the surface roughness was derived and is presented as follows:
𝑦 = 0.8758 − 0.0306𝑥1+ 0.2240𝑥2+ 0.0472𝑥3− 0.0254𝑥4+ 0.0788𝑥1𝑥2
+ 0.0251𝑥1𝑥3 + 0.0980𝑥1𝑥4+ 0.0194𝑥2𝑥3− 0.0841𝑥2𝑥4+ 0.0435𝑥3𝑥4 + 0.2887𝑥12− 0.0363𝑥22− 0.1696𝑥32+ 0.1604𝑥42
Where y represents the surface roughness, 𝑥1 represents the cutting speed, 𝑥2 represents the feed rate, 𝑥3 represents the depth of cut, and 𝑥4 represents the workpiece temperature. Equation 6 represents a quadratic equation for surface roughness modelling based on the actual factors as follows:
𝑅𝑎 = 10.80133 − 0.135718𝑉𝑐 + 3.13054𝑓 + 0.874763𝑎 − 0.028490𝑇 + 0.060052𝑉𝑐
∗ 𝑓 + 0.002006𝑉𝑐 ∗ 𝑎 + 0.000078𝑉𝑐 ∗ 𝑇 + 0.738333𝑓 ∗ 𝑎 − 0.032040𝑓
∗ 𝑇 + 0.001742𝑎 ∗ 𝑇 + 0.000462𝑉𝑐2− 13.15575𝑓2− 0.678442𝑎2 + 0.000064𝑇2
Table 3 presents the predicted values of surface roughness based on the linear and quadratic models for the lathe machining of AISI 4340 using the hot machining method. The predicted values are calculated based on the input values of cutting speed, feed rate, depth of cut, and workpiece temperature. The table also shows the actual values of surface roughness obtained from the experiments conducted. The comparison between the predicted and actual values shows that the models have a good fit with the experimental data, as the predicted values are very close to the actual values. This indicates that the models can be used to predict the surface roughness of AISI 4340 in lathe machining with the hot machining method.
Table 3: Surface Roughness Predicted Value Based on Linear and Quadratic Modelling Using RSM
Table 3 presents the predicted surface roughness values obtained from the linear and quadratic models. The linear model has a percentage error of 20.732% and a mean square error of 0.05228, while the quadratic model has a lower percentage error of 11.7836% and a lower mean square error of 0.019100374.
𝑅𝑎 = 10.80133 − 0.135718𝑉𝑐 + 3.13054𝑓 + 0.874763𝑎 − 0.028490𝑇 + 0.060052𝑉𝑐
∗ 𝑓 + 0.002006𝑉𝑐 ∗ 𝑎 + 0.000078𝑉𝑐 ∗ 𝑇 + 0.738333𝑓 ∗ 𝑎 − 0.032040𝑓
∗ 𝑇 + 0.001742𝑎 ∗ 𝑇 + 0.000462𝑉𝑐2− 13.15575𝑓2− 0.678442𝑎2 + 0.000064𝑇2
After the mathematical equations for linear and quadratic modelling are obtained, the predicted value of surface roughness can be seen in Table 3 above. From Table 3 above in modelling linear surface roughness, the percentage error (%) is 20.732% and the mean square error is 0.05228. Whereas with quadratic modelling the percentage error (%) is 11.7836% and the mean square error percentage is 0.019100374.
The normal probability plot is utilized to assess whether the data gathered from the research follows a normal distribution. To verify the normality assumption, the normal probability plot residual graph is used, as presented in Figure 2. This graph compares the data obtained from the research with a distribution that approximates a normal distribution. If the residual plot is more or less linear, the normality assumption is fulfilled. On the contrary, if the line on the graph slopes to the right or left, the data is not normally distributed. In Figure 2, all points are located near a straight line, indicating that the response surface methodology prediction is accurate.
Figure 2: The Response Surface Methodology Prediction
According to the results presented in Figure 3, the residuals are dispersed randomly and the difference from the original observations remains constant across all y values. This indicates that there is no dependence of the difference in response on the average y level, as there is no funnel-shaped pattern in the plot. Therefore, it can be concluded that the model meets the necessary requirements.
Figure 3: Residuals vs Predicted
Figure 4 is a Perturbation Plot that depicts all the factors included in one response plot. This plot provides information on how the response changes when each factor is moved from a reference point, while keeping all the other factors constant at their reference values.
The impact of different factors on the outcome, including cutting speed (A), feed rate (B), depth of cut (C), and workpiece temperature (D), can be compared at a specific point in the design chamber of the response surface methodology using Figure 4's perturbation chart. In this figure, it can be observed that the slope line for Factor B, i.e., feed rate, is steeper than the slope lines for Factors A, C, and D. This indicates that the response is more sensitive to changes in Factor B, making it an important factor to consider.
5. Conclusion
The analysis of the data indicates that the feed rate has the most significant impact on surface roughness, accounting for approximately 22% of the variation observed in the data. This suggests that changes in the feed rate can result in a substantial difference in surface roughness compared to other factors. Following the feed rate, the depth of cut was found to have a comparatively lower impact on surface roughness, contributing to around 5% of the observed variation. On the other hand, both cutting speed and workpiece temperature were found to have a relatively minor impact on surface roughness, accounting for only about 3% of the variation.
These results highlight the importance of controlling the feed rate while considering surface roughness as the target parameter.
The Response Surface Methodology (RSM) is a widely-used statistical technique that enables researchers to model and analyse the relationship between multiple independent variables and a dependent variable. In the context of surface roughness, RSM can be employed to determine the best mathematical equation that models the relationship between surface roughness and various independent variables, such as cutting speed, infeed rate, depth of cut, and workpiece temperature. After analysing the experimental data obtained through RSM, it has been determined that the Quadratic Model is the most appropriate mathematical equation to predict surface roughness as the dependent variable. The Quadratic Model can be expressed in terms of the independent variables and their interactions, and it can be utilized to optimize the machining process to achieve the desired surface finish. This mathematical equation is a crucial tool for engineers and scientists in the field of manufacturing because it allows them to forecast the surface roughness of a material under different cutting conditions and optimize the machining process to obtain the desired surface finish. The specific form of the Quadratic Model that provides the best fit to the data is:
𝑦 = 0.8758 − 0.0306𝑥1+ 0.2240𝑥2+ 0.0472𝑥3− 0.0254𝑥4+ 0.0788𝑥1𝑥2 + 0.0251𝑥1𝑥3+ 0.0980𝑥1𝑥4+ 0.0194𝑥2𝑥3− 0.0841𝑥2𝑥4
+ 0.0435𝑥3𝑥4+ 0.2887𝑥12− 0.0363𝑥22− 0.1696𝑥32+ 0.1604𝑥42
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