Cutting forces during longitudinal turning process of TI-6AL-4V ELI alloy. Theoretical and experimental values

In the paper, the experimental investigations related with longitudinal turning of Ti-6Al-4V ELI alloy (Grade 23) typically used in aeronautics industry have been presented. The main goal was to determinate the influence of changes in a selected cutting parameters (vc and f) for total cutting force Fc and its components. In this case, the analysis of the components of cutting force Fc measured during workshop experimental investigations was carried out. Next, the measured values were compared with the values calculated on the basis of formulas available in the literature. This allowed one to state that universal theoretical formulas can also be used to determine the components of the total cutting force F in the longitudinal turning process of Ti-6Al-4V ELI alloy.


INTRODUCTION
Machining is the most commonly used technology for the shaping of construction materials, including hard-to-cut materials. This material group includes titanium and titanium alloys, used mainly in the aerospace, medical, automotive, marine and chemical industries [1][2][3][4][5]. This area of application results from the properties which these materials are characterized by. These are: very high corrosion resistance, a high value of strength-to-density ratio, high temperature resistance, high strength under long-term load conditions and biocompatibility [6][7][8][9][10].
A big difficulty in the wide use of titanium alloys is presented by problems in their machining. These problems are related to the occurrence of high cutting temperatures and rapid wear of cutting tools. Available studies from this area [2,3,4,6,11] indicate the main reasons for these problems, including: a low thermal conductivity coefficient, high chemical reactivity with the majority of tool materials, thermoplastic instability during machining, a tendency of chips sticking to the tool, or finally a tendency to create a built-up edge (BUE), which favors the wear of cutting blade. An improvement in the machinability of titanium alloys can be achieved by lowering the cutting temperature. Recommendations for machining titanium alloys indicate the necessity of cutting with a low cutting speed, high feed and depth of cut (in comparison to steel processing) using very sharp tools [6]. For blades made of sintered carbides, is recommended to use a cutting speed of less than 60 m/min at feeds in the range of 0.2-0.5 mm/rev [3]. Another recommendation, to decrease the unfavorably high cutting temperature, is the use of abundant delivering of the cutting fluid. The delivering of machining liquid with a large expense is to extend the tool life by increasing the amount of heat taken over and reducing the cutting forces and improving the removal of chips from the machining zone [3,12].
One of the evaluation methods of the cutting process is based on an analysis of the total cutting force F (crea-ted during machining) and its components. Their values indicate the loading degree of the cutting blade, and thus give an overview of the cutting conditions and the possibility of predicting the tool life period. The values of cutting forces can be determined by means of an experiment and analytical methods.
The main goal of this work is determinate the influence of changes in selected cutting parameters for values of total cutting force and its components during longitudinal turning process of Ti-6Al-4V ELI alloy (Grade 23). In this case, the Author proposes to carry out an analysis of the components of cutting force F c and compare the measured values with the values calculated on the basis of formulas available in the literature. This allowed the Author to state that universal theoretical formulas can also be used to determine the components of the total cutting force F in the longitudinal turning process of Ti-6Al-4V ELI.

CUTTING FORCE IN TURNING
The total cutting force F is the force that affects the workpiece, separates the material and converts it into a chip. The force F can be divided into three directions of the Cartesian coordinate system x, y, z (Fig. 1). The components of the total cutting force F are: F c -cutting force, F f -feed force, F p -back force. The cutting force F c load down the turning tool and causes it to bend, and also affects the mechanism of the cutting inserts fixing. In a similar way, F f affects the tool. In addition, this force attempts to rotate the tool around the axis of the toolholder. Its operation is not very important because it is significantly smaller than the cutting force F c . The resistance force F p is on average about half the value of the force F c .
The components of the total cutting force F can be calculated from various formulas usually determined on the basis of experimental investigations. They may take the form of power formulas (1): where: C c -constant in the formula, z, y, x -power exponents indicating the degree of influence of the parameter on the component of the cutting force. The formulas for the remaining components of the total cutting force are presented in a analogical way. Because the cutting speed has a very small affect on the components of the total cutting force F, the v c parameter is often omitted in the formulas. It should be noted that the more factors are included in the formulas, the more accurately the value of the F force components can be determined. On the other hand, very accurate patterns are only valid for a narrow range of cutting conditions. Therefore, they cannot be transferred directly to other conditions. For this reason, a more simplified formula is often used to determine the cutting forces: where: k c -specific cutting force, N/mm 2 , f -feed, mm/rev, a p -depth of cut, mm. The remaining components of the total cutting force -F f and F p , with regard to turning steel and typical machining conditions, can be determined, with some approximation, from the following formulas: The above formulas - (2), (3) and (4) have the advantage that on their basis, one can determine the force values for any machining conditions. The values of specific cutting force k c for typical machined materials are given in most manuals and books from the area of machining [3,4].

Methodology of experimental investigations
The assessments of the cutting force were carried out during external longitudinal turning of Ti-6Al-4V ELI alloy (Grade 23).
The starting point for the discussion of the Ti-6Al-4V ELI alloy (Grade 23) is Ti-6Al-4V (Grade 5). It is the most commonly used titanium alloy from the group of α+β two-phase alloys [7,13]. Introduction of aluminum to alloy the causes strengthening of the αphase, an increase in the thermal stability of the βphase and a decrease in the density of the alloy [5,6]. The Grade 5 alloy is used mainly in aero-space and medical industries.
Ti-6Al-4V ELI alloy is the highest-purity titanium alloy, i.e. extra low interstitial (ELI). In comparison to Grade 5, it has a lower content of interstitial iron elements, hydrogen and oxygen as well as the resulting better corrosion resistance at the expense of strength. It is also worth remembering that reducing the percentage of oxygen in the alloy causes increases its plasticity and, as a result, increases the cross-section of the chip as a result of improved compression. As a result, the pressure and temperature on the tool edge decrease, which increases its durability [6]. The properties of the Ti-6Al-4V ELI alloy make it widely used in aerospace, aerospace and medical applications (e.g. implants).
In the holder, the cutting inserts -CNMG 12 04 08-SM (Sandvik, Stockholm, Sweden), made of sintered carbides H13A without anti-wear coating were fixed. The manufacturer recommends them mainly for roughing of heat-resistant steels and titanium alloys [12]. The 3-component piezoelectric toolholder dynamometer type 9121 (Kistler, Winterthur, Switzerland) (Fig. 3) measures three components of the total cutting force F: F f -feed force, F p -back force and F ccutting force. In order to correctly register the force F components, the dynamometer was calibrated according to the card provided by the device manufacturer [15].
The investigations were carried out for the cutting parameters presented given in Table 1. The parameters were selected as recommended by Sandvik -the manufacturer of cutting inserts. During the investigations, a metalworking fluid was used. In this case, the Author chose Blasocut emulsion (Blaser Swisslube, Rüegsau, Switzerland) with the coolant flow rate Q CF = 5 l/min. The value of the F c cutting force was calculated on the basis of Formula (5) taken from the SECO information materials published in [16]: The value of k c was calculated from the formula given below (6): where: γ o -orthogonal rake angle, °, k c1.1 -specific cutting force for the selected material, N/mm 2 and m cmaterial factor according to SECO. The values of k c1. 1 and m c were given from the tables available in the SECO catalogue. Their values for titanium-based superalloys are: k c1.1 = 1450 N/mm 2 and m c = 0.23. The value of the nominal thickness of cut h was calculated from the formula given below (7): where: κ r -cutting edge angle, °. The values of the remaining components of the total cutting force were calculated on the basis of Formulas (3) and (4). In Formula (3), the coefficient 0.3 is used, whereas in Formula (4), the coefficient value is 0.5.

Results and discussion
In Figure 4 shows the graph of the course of the components of the total cutting force obtained during the measurement. The course of the cutting force F c is marked in pink, the back force F p in red, and the blue feed force F f . In a character of each of the components can observe the occurrence of leap changes in the level of force value. Because the measurement was carried out by changing the cutting parameter sets in one tool pass, each of the "stairs" (Fig. 4) corresponds to the next set of cutting parameters (the next test). Such a juxtaposition of all components in one graph facilitated the comparison of the variation of the F force components depending on the change of cutting parameters.  Table 2 the results for components of the total cutting force F obtained from the graph above (Fig. 4) were setting up. Based on the results presented in Table 2, can be concluded that for the tested range of cutting data, increasing the feed f at constant cutting speeds v c occurring increases the components F f , F p , F c and total force F.
These differences are similar for individual speeds. The force F values for f = 0.1 mm/rev are ~170% higher from the value for f = 0.4 mm /rev. However, the F force values for f = 0.4 mm/rev are ~90% higher than the value of F for f = 0.25 mm/rev Changes in the cutting speed v c with the same feed change only the total force F by about 2-4%. The above observations and comments are confirmed by the graph in Figure 5.
In this figure, the values of cutting force F c measured for each cutting test were presented. It is widely believed that the cutting force F c is the most representative component in the analysis of machining processes. As is apparent from the literature, the remaining components are less important at the analyses of tool loading by cutting forces. This is mainly due to the highest value of Fc cutting force among all components and the fact that it loads the tool, mainly causing its bending and affects the mechanisms that fix the cutting insert [10]. In Table 3 the values for components of the total cutting force F calculated on the basis of the universal formulas given in Section 3 were setting up. Due to the fact that only the F c component is calculated from the formula, which takes into account the machining conditions, to compare the values of forces measured and calculated to the cutting force F c was used. The graph in Figure 6 shows the measured and calculated values of the cutting force F c .
When comparing the results in Tables 2 and 3 as well as in Figure 6, we see that for feed f = 0.25 mm/ rev (Test 2, 5 and 8) and f = 0.4 mm/rev (Test 3, 6 and 9) the calculated cutting force F c has a lower value