# Modeling and optimization of high-grade compacted graphite iron milling force and surface roughness via response surface methodology.

1. IntroductionHigh tensile strength, thermal fatigue, wear resistance and elastic modulus are key factors that make compacted graphite iron an ideal material for the automobile industry. The superior mechanical properties of this material introduce significant complications during mechanical processing, however, which has hindered its practical application. It's expensive processing cost also represents a heavy burden to the enterprise and to car-owning society.

There has already been a great deal of research on compacted graphite iron wear mechanisms (Heck et al. 2008; Gastel et al. 1999, 2000; Nayyar et al. 2012; Rosa et al. 2010; Silva et al. 2011). Previous researchers have proven that the wear mechanisms of compacted graphite iron are mainly adhesive wear, abrasive wear, diffusion wear and oxidation wear during processing. Modulation-assisted machining technology can assist in cutting processing to prolong the life of cutting tools (Guo et al. 2012); Cutting fluid containing EP additive (Chalcogenide) can be utilised during wet cutting in order to extend tool life (Alves, Schroeter, and Bossardi 2011). Previous research has identified the effects of material mechanical properties and microstructure on the cutting force of compacted graphite cast iron, as well (Nayyar et al. 2013). Apart from a study on the surface quality of compacted graphite cast iron via laser-assisted machining (Liu and Wang 2010;), there has been little research on the surface quality of the material in traditional processing fields (Skvarenina and Shin 2006). The extant research on compacted graphite iron cutting performance mainly centres around the tool wear mechanism and extension of tool life, while studies on the cutting force and surface quality are rare.

Many countries have begun to enforce strict requirements on automobile engine performance to meet the necessary demands for energy savings and emission reduction. Said requirements effectively promote the application of high-grade, compacted graphite iron. Techniques for enhancing the material's processability are, to this effect, highly valuable in today's automobile industry.

In this study, different cutting parameters were employed to process compacted graphite iron RuT400 ([[sigma].sub.b] = 500 MPa) to investigate the cutting force and surface quality of the material. Variance analysis was also employed to analyse the effect of cutting variable on the surface roughness. RSM was used to model the cutting force and surface roughness, then the cutting parameters were optimised according to the prediction model.

2. Experimental procedure

2.1. Workpiece material

The material used in this study is RuT400. Details regarding its performance are provided in Table 1. Its tensile strength is more than 25% higher than RuT400 ([[sigma].sub.b] = 400 MPa) per the Chinese national standard (GB/T 26655-2011). The sample is a 150 mm x 50 mm x 100 mm rectangle with surface roughness of Ra [less than or equal to] 6.3 [micro]m.

2.2. Laboratory equipment

We used a VDL-600A numerical control machining centre (Dalian Machine Group) for the cutting experiment. Its main parameters are shown in Table 2. The face-milling cutter is a BGP-800-FMB27 produced (SandvikCoromant) with a diameter of 80 mm and the milling insert is a APMT 1604 PDER DP5320 super hard sub micro-particle matrix CVD-coated blade (TaeguTec). For the milling test, two blades were symmetrically installed on the cutter head and cutting was operated in the direction of X axis at the centre of the workpiece. Cutting force was measured with an online measurement system consisting of a YDX-III9702-type piezoelectric milling force measuring instrument, YE5850 charge amplifier and data acquisition card. Surface roughness was detected with a SJ-310 surface roughness tester. The cutting experiment apparatus is shown in Figure 1.

2.3. Cutting parameters

Cutting parameters include cutting speed, feeding rate and cutting depth; each parameter has three levels, as shown in Table 3.

3. Results and discussion

We used an orthogonal design method to arrange the level of each variable according to the orthogonal array [L.sub.9]([3.sup.4]) (Camposeco-Negrete 2013). The experiments were carried out randomly. Each test was repeated three times, as shown in Table 4.

3.1. Analysis of variance (ANOVA)

To date, there has been very little research on the cutting performance of compacted graphite cast iron via variance analysis. The effects of the interaction between the cutting parameters are often not considered during analysis of variance of the material cutting performance. Bahurdin et al. (2013), for example, studied the surface quality of spheroidal graphite cast iron without considering the interactive effects of cutting parameters on the surface roughness. Aouici et al. (2012) found that the effect of the interaction between the cutting parameters on the surface roughness is significant in the processing of Hot Work Steel (AISI H11).

We conducted analysis of variance on cutting force and surface roughness first without any interactive effects. The significance of cutting parameters affecting the cutting force and surface roughness was calculated as shown in Tables 4-6. As also shown in Appendix 4 in the Experimental Design section (Shisong et al. 2004), [F.sub.0.90](2, 2) = 9.00, [F.sub.0.95](2, 2) = 19.00, and [F.sub.0.99](2, 2) = 99.00. When the results are judged on a 10% significance level, the F-values of V, f and a are all higher than [F.sub.0.90](2, 2) (Table 5) and cutting speed, feeding rate and cutting depth significantly affect cutting force. The F-values of V are lower than [F.sub.0.95] (2, 2) and [F.sub.0.99](2, 2), indicating that the feeding rate and cutting depth have a significant effect on cutting force while cutting speed does not. The contributions of cutting speed, feeding rate and cutting depth to the cutting force are 2.58, 56.87 and 40.41%, respectively (Table 5); again, the impact of cutting speed on cutting force is negligible compared to that of feeding rate or cutting depth. A significance level of either 5% or 1% is appropriate for our experiment. (Jaharah et al. 2009).

At the 5% significance level, the influence of cutting speed and feeding rate on the surface roughness is considerable while the influence of cutting depth is not (Table 6). At 1% significance level, only the impact of cutting speed on surface roughness is significant. Contribution analysis shows that the contributions of cutting speed, feeding rate and cutting depth to surface roughness are 63.61, 34.56 and 1.24%, respectively. The fact that the feeding rate contribution is above 30% confirms its significant effect on surface roughness.

The above results altogether indicate that 5% is a more reasonable significance level than 1%. Accordingly, feeding rate and cutting depth are the factors that have significant impact on the cutting force while cutting speed and feeding rate are significant factors in surface roughness.

Uncertain factors inevitably affect the results of an experiment such as ours. We built an error term into our ANOVA in order to analyse the influence of this interference. The error term in Tables 5 and 6 includes the uncertainty of random measurement error and the interaction between the cutting parameters and inhomogeneity of the materials. The sums of the squared error are 3.434 and 0.003, respectively, with corresponding contributions of 0.15 and 0.58%. Compared to the other cutting parameters, the sums of the squared error and the contribution of the error term are very small, indicating that uncertain factors exerted only a slight impact on the results. Further, the interactive effects of the cutting parameters on both the cutting force and the surface roughness are not significant, so no further analysis on cutting parameter interactions is necessary.

3.2. Prediction modes

There are two main categories of prediction models for cutting force and surface roughness obtained through RSM. The first involves the use of multivariate linear equation (Mandal et al. 2012; Xiao et al. 2016), and the second involves the use of multivariate linear equation fitting by linearised multivariate non-linear equations (Sahin and Motorcu 2005; Pan et al. 2008; Liu et al. 2010) and can be modelled as follows:

Y = [[beta].sub.0] + [n.summation over (i=1)] [[beta].sub.i][X.sub.i] (1)

The second is:

[mathematical expression not reproducible] (2)

where Y is the response value; [[beta].sub.0] is the constant coefficient of the equation; [X.sub.i] represents the i variable of the model; and [k.sub.i] represents the index of the variable [X.sub.i]. [[beta].sub.0], [[beta].sub.i], C and [k.sub.i] can all be obtained by the least square method.

According to the results presented in Section 3.1, the interactive effects of cutting parameters on cutting force and surface roughness is not significant, so the cutting force and surface roughness prediction model was established without them.

We first built a cutting force prediction model per the requirements of the first category discussed above using the data shown in Table 4:

[F.sub.1] = [[beta].sub.0] + [[beta].sub.1]V + [[beta].sub.2]f + [[beta].sub.3]a (3)

Equation (3) was solved in Design-Expert 8.

[F.sub.1] = 60.823 - 0.020V + 149.489f + 41.932a (4)

The coefficient of determination ([R.sup.2]) of the model and its adjusted correlation coefficient (adj - [R.sup.2]) are 0.996 and 0.994, respectively, so the fitting of the equation is acceptable.

When the second kind of model is used to construct the cutting force prediction model, it is necessary to first linearise the non-linear model. Equation (2) is logarithmic.

ln Y = In C + [n.summation over (i=1)] [k.sub.i] ln [X.sub.i] (5)

The model for predicting the cutting force in Equation (5) was obtained also using the data shown in Table 4:

ln [F.sub.2] = ln C + [k.sub.1] ln V + [k.sub.2] ln f + [k.sub.3] ln a (6)

where [F.sub.2] is the cutting force responsible for the second-category model with a unit of N. Equation (6) was also solved in Design-Expert 8.

ln [F.sub.2] = 5.648 - 0.073 ln V + 0.231 ln f + 0.309 ln a (7)

The following equation can be obtained through an inverse transformation of Equation (7):

[F.sub.2] = 283.723[V.sup.-0.073][f.sup.0.231][a.sup.0.309] (8)

The R[.sup.2] and adj - [R.sup.2] of this model are 0.965 and 0.978, respectively; both are smaller than the first prediction model, suggesting that the prediction accuracy of the second model is inferior. The difference between the predicted values and the measured results is depicted in Figure 2. The prediction values of the cutting force obtained by the first model are much closer to the experimental values i.e., Equation (4) is suitable for accurately predicting the cutting force.

The first prediction equation for surface roughness was obtained via similar analysis on cutting force:

[Ra.sub.1] = 1.633 - 0.00161 V + 1.803f + 0.0289a (9)

where [Ra.sub.1] is the response of surface roughness of the first type of model ([micro]m). The [R.sup.2] and adj - [R.sup.2] of the prediction equation are 0.969 and 0.950, respectively.

The second prediction equation for surface roughness is:

[Ra.sub.2] = 630.807 [V.sup.-0.925][f.sup.0.311][a.sup.-0.022] (10)

where the [Ra.sub.1] is the response of surface roughness of the second type of model ([micro]m). The [R.sup.2] and adj - [R.sup.2] of this model are 0.941 and 0.905, respectively, which are smaller than that of the first equation, again suggesting that the first model yields better prediction accuracy.

The difference between the predicted values and experimental results is shown in Figure 3, where the surface roughness prediction values obtained by the first model are closer to the experimental values than those obtained by the second model; Equation (9) is better suited to the prediction of surface roughness.

In practice, the vibration of the cutting system increases and the surface quality of the machined surface decreases as the cutting force increases (Zeng et al. 2011; Liu et al. 2016; Loftus 2007). As shown in Table 5 and Equation (4), an increase in cutting depth dramatically increases the cutting force thus increasing the surface roughness. The index of cutting depth is less than 0 in Equation (10), however, surface roughness was reduced as the cutting depth increased, which is not reasonable.

3.3. Optimisation of cutting parameters

High cutting efficiency, high workpiece surface quality and a facile cutting process are common practical requirements that are all dependent on the optimisation of cutting parameters. The revolutions per minute of the spindle in the machining process can be calculated according to the cutting speed formula:

n = [1000 V/[pi]D] (11)

where n represents the spindle speed (unit: (r/mm) ) and D indicates the diameter of the cutter head (unit: mm). The rate of the cutting tool's material removal per minute is:

R = [K.sub.1][K.sub.2]Dfna (12)

where [K = 1000[K.sub.1][K.sub.2]/[pi]]. Equations (4), (9) and (13) suggest that it is nearly impossible to obtain the minimum cutting force or surface roughness when the maximum material removal rate is achieved. It is necessary to optimise the cutting parameters appropriately to obtain the maximum material removal rate without sacrificing surface quality and cutting force.

Equations (4), (9) and (13) also indicate that cutting efficiency is high and cutting force/surface roughness are low when cutting speed is high, so it is reasonable to use the maximum cutting speed in the allowable range (V = 753 m/min). According to Equations (4) and (9), when the cutting depth and feeding rate are small, the cutting force and surface roughness are small but the cutting efficiency is low. In practice, surface roughness only needs to be below a certain value to meet the processing requirements. Generally speaking, an economical surface roughness is Ra [less than or equal to] 1.6 or Ra [less than or equal to] 0.8 in the fine milling process.

Similar to surface roughness, as long as the cutting force is in the normal range of cutting tools as such that surface accuracy is appropriate, the process can be considered optimal. We found that cutting force must be below 100 N. According to Equation (4), the response surface and contour map of cutting force at V = 753 m/min are as shown in Figures 4 and 5. The surface roughness response surface and contour map at V = 753 m/min are shown in Figures 6 and 7.

As shown in Figures 4 and 5, the trends of the cutting depth and feeding rate as they affect cutting force are basically the same. The impact of feeding rate on cutting force is slightly greater than that of cutting depth on cutting force. As shown in Figures 6 and 7, the influence of feeding rate on surface roughness is more severe than that of cutting depth, but changes in depth have little impact on surface roughness.

If we preferably consider the parameters which significantly influence the surface roughness when choosing cutting parameters, the maximum feeding rate is 0.1945[micro]m when F [less than or equal to] 100N (Figure 5) and the material removal rate R = 87.87 K([mm.sup.3]/min). Similarly, if we take those parameters which have less impact on surface roughness into consideration, the maximum cutting depth is 0.9369 mm when F [less than or equal to] 100 N and the material removal rate is R = 70.55 K([mm.sup.3]/min) (Figure 5). The material removal rate is 24.55% higher in the former than the latter. In short: the parameters which have greater influence on cutting effect should be given higher priority during cutting parameter optimisation.

We also calculated the optimal value of cutting parameters in LINGO1 software under the constraint conditions described above. The first optimised output is shown in Figure 8. The maximum material removal rate is defined as the following objective function:

W = max R = max (KVfa) (14)

As K is independent of the cutting parameters and its coefficient is more than 0, it is treated as a constant when optimising the cutting parameters. The remaining constraint conditions are as follows:

[mathematical expression not reproducible] (15)

Equation (14) was solved in LINGO1 software under the constraint conditions described in Equations (15)-(19). The results are shown in Table 7. The obtained material removal rate is consistent with the material removal rate obtained by the response surface and contour map, suggesting that the two optimisation methods have similar optimisation accuracy.

Table 7 shows that there is a 0.034 [micro]m difference between the optimal value and upper bound limit of surface roughness. If the constraint of cutting force increases to 120 N, the constraints are as follows:

[mathematical expression not reproducible] (16)

The solution of Equation (14) calculated in LINGO1 under the constraint conditions of Equation (16) is shown in Table 8.

According to Tables 7 and 8, when the allowable cutting force is increased by 20%, the material removal rate increases 76.51%, while the surface roughness increases only 3.45%. This marks a significant improvement in production efficiency. The influence of cutting force on tool life and on the rigidity of the processing system is the main restrictions on the cutting force. When the processing system has favourable rigidity, the use of cutting tools with high strength and minimal cutting force can greatly enhance the machining efficiency.

4. Conclusions

(1) Variance analysis of cutting parameters indicated that both feeding rate and cutting depth significantly influence cutting force; cutting speed and feeding rate have significant impact on surface roughness.

(2) The prediction accuracy of the cutting force and the surface roughness prediction model obtained by fitting multiple linear equations is higher than that of the model obtained by fitting the multivariate non-linear equation.

(3) The cutting force prediction and surface roughness prediction models based on RSM are F = 60.823 - 0.020V + 149.489f + 41.932a and Ra = 1.633 - 0.00161V + 1.803f + 0.028 9a, respectively.

(4) The optimal solution obtained by the response surface and contour plots was similar to that of the optimal solution calculated in LINGO1 software.

(5) When the system has favourable rigidity, the use of tools with high strength and high endurance of the manufacturing system undercutting force can greatly enhance the machining efficiency.

Funding

This project was supported by Natural Science Foundation of Guangxi Province [grant number 2014GXNSFAA118347]; Science and Technology Co-funded project of Guangxi University and Yulin City (Yulin City-School Science and Technology Co.) [grant number 201402801].

Notes on contributors

Yongchuan Lin received his doctoral degree in Innovative Technology and Science from Kanazawa University, Japan. He is presently the associate professor of Guangxi University, China. He has academic experience in high-speed machining technology.

Jianyou Huang is a master's student at Guangxi University; his research focus is Advanced Manufacturing Technology.

Jueyu Wei is a master's student at Guangxi University; his research focus is Material Processing.

Xiaoping Liao received his doctoral degree from Huazhong University of Science and Technology, China. He is presently the General Secretary and Professor of Mechanical Engineering at Guangxi University. He has academic experience in Theory of Modern Digital Design.

Zeqing Xiao is a doctoral student at Guangxi University; his research focus is Quality Prediction and Control.

ORCID

Yongchuan Lin http://orcid.org/0000-0003-1161-4473

Jianyou Huang http://orcid.org/0000-0001-5914-5763

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Yongchuan Lin (a), Jianyou Huang (a), Jueyu Wei (a), Xiaoping Liao (a) and Zeqing Xiao (b)

(a) College of Mechanical Engineering, Guangxi University, Nanning, China; (b) Institute of Light Industry and Food Engineering, Guangxi University, Nanning, China

CONTACT Jianyou Huang huangjianyou2000@163.com

ARTICLE HISTORY

Received 10 July 2016

Accepted 13 February 2017

https://doi.org/10.1080/14484846.2017.1296531

Table 1. Material properties. Tensile Friction strength Elongation Hardness Material coefficient (MPa) (%) (HB) RuT400 0.212 513.7 0.925 215 Table 2. Parameters of CNC machining centre (VDL-600A). X and Y cutting speed range Spindle speed range r/min Spindle power kW mm/min 60~8000 7.5 1~10000 Spindle speed range r/min X and Y power kW Maximum tool diameter mm 60~8000 3 [phi]100 Table 3. cutting parameters and levels. Cutting Symbol parameter Unit Level 1 Level 2 Level 3 V cutting speed m/min 452 602 753 f Feeding rate mm/r 0.1 0.2 0.3 a cutting depth mm 0.6 0.9 1.2 Table 4. Variable combinations and test results. Surface Cutting force roughness Ra No. Test sequence V f a F(N) ([mucro]m) 1 8th 1 1 1 91.40 1.096 2 2nd 1 2 2 117.77 1.256 3 7th 1 3 3 146.90 1.464 4 3rd 2 1 2 101.60 0.858 5 6th 2 2 3 130.62 1.108 6 4th 2 3 1 119.97 1.312 7 5th 3 1 3 110.58 0.664 8 1st 3 2 1 100.65 0.776 9 9th 3 3 2 126.39 0.924 Table 5. ANOVA results for cutting force. Sum of Mean Cont. Source squares DF square F-value % Remarks V 60.711 2 30.356 17.678 2.58 Significant f 1339.772 2 669.886 390.120 56.87 Significant a 951.990 2 475.995 277.204 40.41 Significant Error 3.434 2 1.717 0.15 Total 2355.908 8 100 Table 6. ANOVA results for surface roughness. Sum of Mean Cont. Source squares DF square F-value % Remarks V 0.359 2 0.180 108.992 63.61 significant f 0.195 2 0.098 59.224 34.56 significant a 0.007 2 0.004 2.131 1.24 Not significant Error 0.003 2 0.002 0.58 Total 0.565 8 100.00 Table 7. Optimisation results ([F.sub.1] [less than or equal to] 100). V f a F Ra R m/min mm/min mm n [micro]m [mm.sup.3[/min 753 0.1814 0.6467 99.998 0.766 88.34 K Table 8. Optimisation results (F [less than or equal to] 120). V f a F Ra R m/min mm/min mm N [micro]m [mm.sup.3]/min 753 0.1866 1.098 119.998 0.7924 155.93 K

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Author: | Lin, Yongchuan; Huang, Jianyou; Wei, Jueyu; Liao, Xiaoping; Xiao, Zeqing |
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Publication: | Australian Journal of Mechanical Engineering |

Geographic Code: | 9CHIN |

Date: | Mar 1, 2018 |

Words: | 4547 |

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