Optimization of dry turning process parameters of titanium alloy based on response surface methodology

Bing-qi HUANG, Jian-bing MENG, Xiao-juan DONG, Yan-mei ZHANG, Yi-zhong HU, Xiao-sheng LUAN, Ru-feng XU

(School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China)

Abstract: In order to improve the dry turning quality of titanium alloy, the response surface methodology was used to optimize the main turning parameters. A Box-Behnken experimental model was developed the cutting speed, cutting depth and feed rate were regarded as the processing parameters,Ra of workpiece surface roughness and VC of tool wear were regarded as evaluation indexes. Variance and fitting residual probability distribution were used to analyze the significance and interaction of three factors. Furthermore, the validity of the second-order response prediction model of surface roughness and tool wear was verified by experiments. The result shows that the optimum cutting speed, cutting depth and feed rate is 20 m/min, 0.178 8 mm, 0.1 mm/r, respectively. The surface roughness and tool wear obtained by cutting with optimized three parameters, is 1.031 μm, 155.6 μm, The errors are 9.93% and 1.58% respectively compared with predicted value. It is proved that the prediction model of surface roughness and tool wear based on response surface methodology(RSM) is accurate and effective.

Key words: Titanium alloy,Response surface methodology(RSM), Drying turning, Technological parameter optimization

Titanium alloy has been widely used in aviation, aerospace, ship, automobile and other fields because of the advantages of corrosion resistance, high temperature resistance and high specific strength. However, low thermal conductivity and small elastic modulus of titanium alloys are some problems in cutting process, which can cause tool wear rapidly and surface quality is difficult to guarantee[1-3]. In dry cutting process of titanium alloy, tool wear is particularly obvious[4-6]. How to reduce tool wear and improve workpiece surface roughness has become an urgent problem in dry cutting of titanium alloy.

Hou [7] designed two steps (rough-finishing)and three steps (rough-semi-precision-finishing) turning process for titanium alloy based on single factor experiments， and analyzed the influence of the change of cutting parameters in the first two steps on the surface quality of finish machining. Koseki [8] studied the wear mechanism of PVD coated cutting tools in Ti6Al4V continuous turning process and the damage factors and modes of cutting tools were analyzed. Nithianandam [9] reported the influence of cutting speed, feed speed, tool tip radius and cutting depth on surface roughness by variance analysis and signal-to-noise ratio. It can be seen that the selection of the above process parameters not only affects the processing quality and tool life of titanium alloy dry turning, but also directly determines the processing cost and efficiency. However, at present, the optimization of process parameters is mainly limited to the effect of single factor on processing index [10-12], which ignore the comprehensive effect of multi-factors and the interaction of multi-factors on processing index.

In this paper, the cutting speedv, the cutting depthαpand the feedfin the dry turning of TC4 titanium alloy are used as the independent variables to be optimized. The tool wear value and the surface roughness of the workpiece are used as processing indexes. Based on the relevant experimental scheme of Box-Behnken Design response surface method [13-15], the second-order prediction model of tool wear and workpiece surface roughness with respect to three independent variables is established by variance analysis. Moreover, parameters are optimized to obtain the best turning process parameters for providing some theoretical guidance for titanium alloy dry turning.

1 Experimental device

The CKD6136i CNC lathe was used in the experiment, the lathe shown in Fig.1(a). The TC4 Titanium Alloy cylinder as workpiece was used in the experiment, the coated carbide turning tools (SNMG120404 VP15TF Japan Mitsubishi Corporation) and the 40Cr arbor (MSDNN2020K12, China Kapulada Corporation) have been applied in the experiment. Cutting schematic is shown in Fig.1(b). The amount of main cutting edge flank maximum(VC) has been measured by a digital microscope (Germany Zeiss),VCis shown in Fig.1(c). The tool main deflection angle 45 degrees, sub-deflection angle 45 degrees, rake angle 0 degree, rear angle 0 degree, edge inclination 9 degrees after clamping have been applied in the experiment.

Fig.1 Dry turning device for titanium alloy and its processing test schematic diagram

The surface roughnessRaof the workpiece after turning was measured by TR200 hand-held roughness meter. The following mathematical characterization was carried out: dry turning test was carried out with the combination of cutting speed, cutting depth and feed rate as three process parameters. Each turning distance was 800 meters as the standard. The cutting distance can be expressed as:

(1)

In the formula,Lis the cutting distance, unit m;Vis the cutting speed, unit m/min;Zis the processing length, unit mm;nis the speed, unit r/min;fis the feed, unit mm/r.

2 Experimental design

On the basis of single factor test and analysis, cutting speedv, the cutting depthαpand feed ratefwere selected as the optimized parameters, which were set as independent variablesx1,x2andx3in turn. The process parameters range was divided respectively: [20, 60], [0.1, 0.3], [0.1, 0.2], and each independent variable was selected at -1, 0 and 1 levels. The surface roughness valueRaand tool wearVCwere taken as the corresponding response values, gaining three-factor and three-level test scheme, as shown in Table 1.

Table 1 BBD Test factors and levels

Box-Behnken Design method was used to design five centers on the basis of Table 1, and the corresponding combination of independent variables parameters was obtained. Dry turning of titanium alloy was carried out according to the combination of parameters. The surface roughness of workpiece was measured by roughness meter, and the average value of five times was taken as the final value ofRa. The tool wear value was observed by electron microscope. The BBD test scheme and corresponding results are shown in Table 2.

Table 2. BBD Test scheme and results

3 Prediction model

Response Surface Methodology (RSM) was used to establish multiple second-order regression prediction models of workpiece surface roughnessRaand tool tip flankVCwith respect to independent variablesx1,x2andx3respectively. As shown in formulas (2) and (3), it is helpful to analyze the influence of three main process parameters: cutting speed, the cutting depth and feed rate on processing indexesRaandVC.

Ra=1.424+0.353x1-17.76x2-3.70x3-

0.030 9x1x2-0.198 5x1x3-19.2x2x3

(2)

VC=101.24+0.998x1+209.0x2+41.3x3-

0.187x1x2-3.250x1x2-355x2x3

(3)

The response values ofRaandVCto independent variablesx1,x2andx3were analyzed by variance analysis as shown in table 3 and 4. Among them,Pvalue does not reject the original hypothesis if less than 0.05 it shows that the model is significant. In Table 3 and 4, there are more items withPvalue less than 0.05, hence there are such more significant items that the fitting equation has a higher significance. In addition, the confidence interval of 95% in Table 3 is 5.05 [15], and theFvalue of misstatement test is 3.99, which less than 5.05. It can be considered that the model is reliable. The value of multielement correlation coefficientR2is 98.80% close to 1 and the adjusted value of multielement correlation coefficientR2is 97.25%, the two values are close, so it can be concluded that theRaprediction model fits well; theFvalue of misstatement test in Table 4 is 2.96, also less than 5.05, and the multielement correlation coefficientR2is 97.25%. The value ofR2is 98.95%, closer to 1, and the adjusted multi-element correlation coefficientR2is 97.60%. The two values are also close, so the reliability of tool wear prediction model established by response surface method is also high.

Table 3 Variance Analysis of Ra Prediction Model

Table 4 Ra predictive model misclassification test and model summary

Table 5 Variance Analysis of VC Prediction Mode

Table 6 VC predictive model misclassification test and model summary

The probability distribution of fitting residuals for the responses of independent variablesx1,x2andx3toRaandVCwas analyzed. The distribution of residuals is shown in Figure 2.

From Fig.2 (a), it can be seen that some scatters on both sides deviate from the fitting line, but most of them are distributed near the predicted line, and the scatters deviate from the straight line slightly, which proves that the prediction model of surface roughnessRaabout three independent variables of cutting speed, the cutting depth and feed rate work well. The probability distribution of fitting residual of tool wearVCis shown in Fig.2 (b). Although the right part of scatter points deviates from the fitting line, most scatter points are close to the fitting line, which shows that the prediction model of tool wearVCfor three independent variables, cutting speed, back feed and feed, is also reliable and can be used for the optimization of independent variablesx1,x2andx3.

Fig.2 Normal probability plot of Response item residuals

4 Result analysis

There are three variables and two response optimization objectives in the experiment. Three variables are interacted with each other and significant interaction terms are selected to design response surface. Independent variables are set tox-axis andy-axis respectively, as well as the response value isz-axis. Another independent variable is set to the intermediate value of variables. Response surface is established through Minitab. Figures 3 (a) and 3 (b) show the cutting speed and feed rate on response surface and contour map of surface roughnessRa. It can be easily foundRadecreases with the increase of cutting speed under the condition that the cutting depth is equal to 0.2 mm, which because the dry turning of titanium alloy will produce chip tumors and spines when the cutting speed is low, causingRato increase. With the increase of cutting speed, the chip tumors decrease and the plastic deformation of the machined surface is insufficient, which reduces the surface roughnessRa.

Formula (4) shows that theRaof workpiece raise with the increase of feed rate. With the increase of feed rate, chip accumulation and bond wear of cutting tools will increase correspondingly, and vibration will easily occur. Because the cutting depth is not significant for the surface roughness prediction model, it has little effect on the surface roughness.

(4)

In the formula,Rais the surface roughness of the workpiece andrεis the cutter tip arc radius.

Fig.4 (a) and 4 (b) are the response surface and contour diagrams of tool wearVCrelative to cutting speedVand feed ratef, respectively. In the diagrams, the cutting depthαpthat equals to 0.2 mm remains unchanged. It can be seen from the figure that tool wear increases with the raise of cutting speedvand feed ratefrespectively. This is because the increase of cutting speedvleads to the increase of cutting heat and cutting force, which aggravates tool wear; The increase of feed rate f will lead to the probability of chip accumulation and cutting vibration, which will also lead to the increase of tool wear.

Fig.4 (c) and (d) are the response surface and contour diagrams of tool wearVCrelative to the cutting depthαpand feed ratefrespectively. The diagrams keep cutting speedvequal to 40 m/min. It can conclude from the figure that the increase of the cutting depthαpwill lead to the increase of tool wear. This is because the influence of the cutting depth on cutting force is more obvious, tool wear will increase with the raise of the cutting depth.

5 Parameter optimization and verification

Combined with the response surface analysis ofRaandVCin Fig.3 and Fig.4, the optimal target was designed and then the second-order response surface equation ofRaandVCwas calculated to obtain the optimal technological parameters during the dry turning of titanium alloy. Among them, the optimization principle is to obtain the best workpiece surface and the lowest tool wear, using Minitab response optimizer as the optimization tool as well as the 17 test data of BBD method as the optimization target. The optimization results of roughnessRaand tool wearVCare 0.764 μm and 153.1 μm respectively. The optimum combination of the corresponding process parameters is shown in Fig.5, i.e. the cutting speedv, the cutting depthαpand feed ratefare 20 m/min, 0.178 8 mm and 0.1 mm/r respectively. Taking the optimized process parameters combination as independent variablesx1,x2,x3and substituting them into formulas (2) and (3), the predicted values of surface roughnessRaand tool wearVCare 0.926 8 μm and 153.142 2 μm. The satisfactiondof the two variables is 0.932 26 and 0.998 70 likewise the overall satisfactiondis 0.964 9.

Fig.3 Response surface and contour plots of surface roughness Ra

Fig.4 Response surface and contour plots of tool wear VC

Fig.5 Process parameters optimization results based on response surface methodology

The optimized independent variablesx1=20 m/min,x2=0.178 8 mm,x3=0.1 mm/r were used as cutting parameters to verify the experiment. The roughnessRaobtained was 1.031um, at the same time the error compared with the predicted value of 0.928 6 μm was 9.93%. Fig.6 (a) is the actual tool wear situation when cutting speedv, the cutting depthαpand feed ratefare 20 m/min, 0.178 8 mm and 0.1 mm/r respectively. Fig.6 (b) is the workpiece surface under the optimized cutting parameters. Fig.6 (c) and (d) are the workpiece surface topography under the optimized parameters in BBD test. The surface topography of Fig.6 (b) is obviously better than that of Fig.6 (c), (d). From Figure 6, it can be concluded that the tool wear valueVCis 155.6 μm, and the error between the real value and the predicted value 153.142 2 μm is 1.58%. Obviously, the theoretical values of surface roughnessRa, tool wearVCand response surface prediction model have good coincidence accuracy with the optimized combination of independent variables as cutting parameters.

Fig.6 Tool wear and workpiece surface after optimizing

6 Conclusions

(1) Significant analysis by BBD test on dry cutting parameters of titanium alloy is proposed in this paper. The order of significant influence on the surface roughnessRais obtained: feed ratef, cutting speedvand the cutting depthαp; and the order of remarkable influence on tool wear: depthαp, feed ratef, and cutting speedv.

(2) Second-order regression equation prediction models for surface roughness and tool wear were established respectively. Analysis of variance and normal probability distribution analysis of the model.The analysis results show that the prediction model has a high degree of fitting and good fitting effect.

(3) The cutting speedv, the back-feeding amountαp, and the feed amountfare used as independent variables. The surface roughness valueRaand the tool wearVCare used as response items, the response target value is set, and the response surface analysis is performed to obtain the optimal combination of cutting parameters:v= 20 m/min,αp=0.178 8 mm,f=0.1 mm/r; The optimized combination of independent variables is used as the cutting parameter. The error of the obtained surface roughnessRa, tool wearVCand predicted value are all within a reasonable range, and the feasibility of the response surface method is verified.