The experiments were conducted on the CNC milling center DMG DMU80P. The block with dimensions of 145 × 100 × 80 mm made of Hadfield steel (110G13L) was used as a workpiece. The chemical composition is presented in Table 1. The workpiece was fastened on the Kistler 9253B multicomponent dynamometer insert installed on the machine table (Fig. 1). Using this insert, the cutting forces were measured. The milling direction was associated; the cutting pattern was ledge-type. Experimental cuts were made at three different cutting speeds Vc=90, 120 and 150 m/min and three different feeds fz=0.09, 0.12 and 0.15 mm/rev.
The Sandvik R390-020C3-11M050 cutter was used as a cutting tool. Inserts R390-11 T3 31M-PM of the same geometry, made of S30T, S40T, 1130 and 4240 hard alloys were alternately installed on the cutter (Table 2). Each carbide grade has a unique protective coating and chemical composition. Each type of coating was applied by different methods. In order to eliminate the influence of the cutting edge, only one insert was installed [12].
Table 2
Parameters | Grade |
S30T | S40T | 1130 | 4240 |
Coating | PVD TiAlN | CVD TiCrN + Al2O3 + TiN | PVD AlTiCrN | CVD TiCN + Al2O3 + TiN |
Corner radius (mm) | 3.1 | 3.1 | 3.1 | 3.1 |
Effective length of the cutting edge (mm) | 10 | 10 | 10 | 10 |
Major cutting edge angle (deg) | 90 | 90 | 90 | 90 |
Cutting forces Fx, Fy and Fz were measured in the milling process. The milling scheme and cutting force directions are shown in Fig. 2.
With the cutting insert wear, the axial and active forces increase. The active cutting force Fa was calculated taking into account that Fx=Ff, Fy=FfN using formula \({F}_{a}=\sqrt{{F}_{f}^{2}+{F}_{fN}^{2}}\).
The experiment was planned based on the robust plan Taguchi L 18 (21 × 32). The Taguchi method involves the use of the signal-to-noise ratio to characterize the process. The signal is a change in the properties of product y under the influence of controlled factors x, and noise is a deviation of y (characterized by variance s2) due to the influence of uncontrolled factors z. There are several qualities to analyze the process [25]:
-
The logarithmic function of variance:
$$\frac{S}{N}=-10\text{log}{s}^{2}$$
- The signal-to-noise ratio:
$$\frac{S}{N}=10\left(\frac{{y}^{2}}{{s}^{2}}\right)$$
- More-less:
$$\frac{S}{N}=-10\text{log}\left[\frac{\sum {y}^{-2}}{n}\right]$$
- Smaller-better:
$$\frac{S}{N}=-10\text{log}\left[\frac{\sum {y}^{2}}{n}\right]$$
In the current study, the “Less is better” quality was used.
A change in the active force Fa under the influence of controlled factors acted as a signal: A was the alloy grade, B was the cutting speed, C was the feed, and Fa deviation was the noise.
Carbide inserts of S30T, S40T and 1130, 4240 grades, cutting speed Vc, feed fn (fn=fz) were selected as variable parameters, whose values are presented in Tables 3 and 4. The milling parameters were determined based on the cutting tool manufacturer's recommendations.
Table 3
Milling parameters and their levels.
Parameters | Symbol | Level 1 | Level 2 | Level 3 |
Grade | A | S30T | 1130 | – |
Cutting speed, Vc (m/min) | B | 90 | 120 | 150 |
Feed rate, fn (mm/rev) | C | 0.09 | 0.12 | 0.15 |
Table 4
Milling parameters and their levels.
Parameters | Symbol | Level 1 | Level 2 | Level 3 |
Grade | A | S40T | 4240 | – |
Cutting speed, Vc (m/min) | B | 90 | 120 | 150 |
Feed rate, fn (mm/rev) | C | 0.09 | 0.12 | 0.15 |
For each pair of hard material inserts, the experiment was based on a mixed orthogonal matrix (Table 5). The experimental plan and values of the cutting parameters are presented in Tables 6–7.
Table 5
The factorial plan with an orthogonal array Taguchi L18 (21 × 32)
Experiment no. | Factor A | Factor B | Factor C |
1 | 1 | 1 | 1 |
2 | 1 | 1 | 2 |
3 | 1 | 1 | 3 |
4 | 1 | 2 | 1 |
5 | 1 | 2 | 2 |
6 | 1 | 2 | 3 |
7 | 1 | 3 | 1 |
8 | 1 | 3 | 2 |
9 | 1 | 3 | 3 |
10 | 2 | 1 | 1 |
11 | 2 | 1 | 2 |
12 | 2 | 1 | 3 |
13 | 2 | 2 | 1 |
14 | 2 | 2 | 2 |
15 | 2 | 2 | 3 |
16 | 2 | 3 | 1 |
17 | 2 | 3 | 2 |
18 | 2 | 3 | 3 |
Table 6
The experiment results (S30T and 1130)
Experiment no. | Control factors | Active force, Fa (N) | Fa for S/N ratios |
A | B | C |
Grade | Cutting speed (Vc) | Feed rate (fn) |
1 | S30T | 90 | 0.09 | 262,8 | -48,3933 |
2 | S30T | 90 | 0.12 | 338,7 | -50,5971 |
3 | S30T | 90 | 0.15 | 384,9 | -51,7059 |
4 | S30T | 120 | 0.09 | 257,7 | -48,2223 |
5 | S30T | 120 | 0.12 | 319,9 | -50,0997 |
6 | S30T | 120 | 0.15 | 373,3 | -51,4414 |
7 | S30T | 150 | 0.09 | 255,1 | -48,1349 |
8 | S30T | 150 | 0.12 | 287,6 | -49,1768 |
9 | S30T | 150 | 0.15 | 355,8 | -51,0233 |
10 | 1130 | 90 | 0.09 | 317,0 | -50,0208 |
11 | 1130 | 90 | 0.12 | 345,1 | -50,7591 |
12 | 1130 | 90 | 0.15 | 407,3 | -52,1976 |
13 | 1130 | 120 | 0.09 | 299,5 | -49,5291 |
14 | 1130 | 120 | 0.12 | 358,1 | -51,0791 |
15 | 1130 | 120 | 0.15 | 342,4 | -50,6899 |
16 | 1130 | 150 | 0.09 | 255,6 | -48,1495 |
17 | 1130 | 150 | 0.12 | 300,2 | -49,5470 |
18 | 1130 | 150 | 0.15 | 347,3 | -50,8151 |
Table 7
The experiment results (S40T and 4240)
Experiment no. | Control factors | | | Active force, Fa (N) | Fa for S/N ratios |
A | B | C | |
Grade | Cutting speed (Vc) | Feed rate (fn) | |
1 | S40T | 90 | 0.09 | | 337,5 | -50,5650 | |
2 | S40T | 90 | 0.12 | | 395,0 | -50,5650 | |
3 | S40T | 90 | 0.15 | | 451,1 | -50,5650 | |
4 | S40T | 120 | 0.09 | | 324,2 | -50,5650 | |
5 | S40T | 120 | 0.12 | | 401,8 | -50,5650 | |
6 | S40T | 120 | 0.15 | | 409,5 | -50,5650 | |
7 | S40T | 150 | 0.09 | | 274,2 | -50,5650 | |
8 | S40T | 150 | 0.12 | | 316,4 | -50,5650 | |
9 | S40T | 150 | 0.15 | | 360,7 | -50,5650 | |
10 | 4240 | 90 | 0.09 | | 393,1 | -50,5650 | |
11 | 4240 | 90 | 0.12 | | 650,8 | -50,5650 | |
12 | 4240 | 90 | 0.15 | | 398,2 | -50,5650 | |
13 | 4240 | 120 | 0.09 | | 318,8 | -50,5650 | |
14 | 4240 | 120 | 0.12 | | 361,9 | -50,5650 | |
15 | 4240 | 120 | 0.15 | | 392,6 | -50,5650 | |
16 | 4240 | 150 | 0.09 | | 463,6 | -50,5650 | |
17 | 4240 | 150 | 0.12 | | 315,6 | -50,5650 | |
18 | 4240 | 150 | 0.15 | | 340,1 | -50,5650 | |
The influence of variable parameters on the active cutting force was analyzed using the "S/N response table" (Table 8 and Table 9). The tables show optimal values of the variable parameters for the minimum active cutting force. The values of the control factors for Fa shown in Tables 8 and 9 are presented in Figs. 3 and 4. The graphs were used to determine optimal values of the control factors to minimize the active cutting force. The best level for each control factor was determined for the highest S/N ratio. The S/N levels and ratios for the factors providing the lowest Fa value are: for the group of S30T and 1130 carbide inserts, for factor A -level 1, S/N=-49.87, for factor B -level 3, S/ N=-49.47), for factor C – level 1, S/N=-48.74; for the group of S40T and 4240 inserts, for factor A -level 1, S/N=-51.12, for factor B -level 3, S/N=-50.64-), for factor C – level 1, S/N =-50.80.
Table 8
S/N response table for Fa factor (S30T and 1130)
Level | A | B | C |
1 | -49.87 | -50.61 | -48.74 |
2 | -50.31 | -50.18 | -50.21 |
3 | - | -49.47 | -51.31 |
Delta | 0.44 | 1.14 | 2.57 |
Table 9
S/N response table for Fa factor (Grade S40T and 4240)
Level | A | B | C |
1 | -51.12 | -52.62 | -50.80 |
2 | -51,91 | -51,28 | -51.91 |
3 | - | -50.64 | -51.83 |
Delta | 0.80 | 1.98 | 1.10 |
Based on the data in Tables 8 and 9 and the graphs in Figs. 3 and 4, the optimum Fa value was determined for milling with a S30T carbide insert (Vc = 150 m/min and fz = 0.09 mm/ tooth) and a S40T carbide insert (Vc = 150 m/min and fz = 0.09 mm/tooth).
Using the results obtained, S30T and S40T carbide inserts were compared. The results are presented in Table 10 and Fig. 5. An analysis of the levels and S/N ratios revealed that in milling of Hadfield steel, S30T carbide inserts with a minimum S/N ratio of 49.87 should be used.
Table 10
S/N response table for Fa factor (S30T and 1130)
Level | A | B | C |
1 | -49.87 | -51.05 | -49.05 |
2 | -51.12 | -50.72 | -50.65 |
3 | - | -49.71 | -51.77 |
Delta | 1.25 | 1.34 | 2.72 |
The variance analysis is used to determine the individual interactions of all controlled factors. In the current study, the variance analysis was used to study the effect of carbide inserts, cutting speed and feed on the active cutting force. The results are presented in Table 11. The analysis was carried out with a significance level of 5% and a confidence level of 95%. Table 11 shows that the percentage contributions of factors A, B, and C to the active cutting force were 21.37%, 7.45%, and 65.22%, respectively. Thus, the most important factor influencing the active cutting force was the tool feed (factor C, 65.22%). The error rate was significantly lower − 5.95%.
Table 11
Results of ANOVA for the Active Cutting Force
Variance source | Degree of freedom (DoF) | Sum of squares (SS) | Mean square (MS) | F-Value | Contribution rate (%) |
Fa |
A | 1 | 10500 | 10500 | 3.69 | 21.37 |
B | 2 | 9196 | 3123 | 1.47 | 7.45 |
C | 2 | 32557 | 16278 | 10.40 | 65.22 |
Error | 51 | 10805 | 211.9 | | 5.95 |
Total | 53 | 181297 | | | 100 |
The regression analysis was applied to model and analyze dependent and independent variables. The dependent variable is active cutting force Fa; the independent variables are cutting speed and tool feed. The prognostic equation is presented below. The values of the coefficient of equation determination, which was obtained using the linear regression model for Fa, were 91.82% and 90.07%, respectively.
Fa = 165,6 + 48,30 A − 0,890 B + 1732 C
R-Sq = 91.82% R-Sq(adj) = 90.07%
Figure 6 compares the actual test results and the predicted values obtained using the linear regression model. As can be seen, there is a relationship between the predicted values and the test results.
The dependences of cutting forces on cutting data obtained by the regression analysis are shown in Fig. 7. The graph for the S30T grade (Fig. 7a) shows that the dependence of cutting force on feed and cutting speed is linear for all the cutting data. With an increase in the feed, the cutting force increases proportionally, which is consistent with the cutting theory. With an increase in the cutting speed, the cutting force decreases due to a decrease in the strength of the material affected by the temperature in the cutting zone, which grows with increasing cutting speed values. These results make it possible to predict values of the cutting force when using S30T grade inserts. If the satisfactory tool life is achieved at maximum cutting parameters, S30T inserts can be used for machining Hadfield steel parts.
The graph for the S40T grade (Fig. 7b) shows that the dependence of cutting forces on feed is close to linear and cutting force values are higher than for the S30T grade over the entire feed range. The dependence of cutting forces on cutting speed is parabolic, reaching maximum values in the speed range Vc=110–115 m/min. It can be assumed that in the specified range of cutting speeds, the build-up of material affects the cutting edge. When using S40T inserts at maximum feed values, the cutting force is higher by about 5%.
The dependences of cutting forces on feed and cutting speed for 1130 grade inserts (Fig. 7c) are similar to the dependences obtained for S30T grade inserts. At the same time, the cutting forces measured at maximum cutting parameters are approximately 4% lower than those for S30T grade inserts. These results indicate that the 1130 grade is a promising tool material for Hadfield steel. Along with the S30T alloy, it requires additional testing for durability.
The cutting force plot for the 4240 grade (Fig. 7d) is non-linear. The hyperbolic dependence of cutting forces on cutting speed is combined with a parabolic dependence on feed. This indicates a significant influence of cutting modes on the chip interacting with the insert surface. This fact makes it difficult to predict changes in cutting forces depending on the cutting parameters. When using the 4240 grade, the cutting force exceeds the one measured when using other alloys. The minimum value of the cutting force was measured at Vc=120 m/min. This means that in some cases the machining performance should be reduced by at least 30% in order to ensure a minimum load on the technological system.