Vibration analysis of cutting force in titanium alloy milling

ARTICLE IN PRESS International Journal of Machine Tools & Manufacture 50 (2010) 65–74 Contents lists available at ScienceDirect International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool Vibration analysis of cutting force in titanium alloy milling Armando Italo Sette Antonialli a,, Anselmo Eduardo Diniz b,1, Robson Pederiva b,1 a b ~ Carlos, SP, Brazil ~ Carlos, 13565-905 Sao Materials Engineering Department, Federal University of Sao Faculty of Mechanical Engineering, State University of Campinas, C. Postal 6122, 13083-860 Campinas, SP, Brazil a r t i c l e in fo abstract Article history: Received 16 June 2009 Received in revised form 1 September 2009 Accepted 8 September 2009 Available online 16 September 2009 Machining processes such as milling, which are characterized by interrupted cutting, are often susceptible to problems involving vibration of the machine-tool-workpiece fixation device system because of the proximity between their natural frequency harmonics and the frequency of tool entry on the workpiece. This phenomenon is particularly important in the milling of titanium alloys, because these materials show a low Young modulus, and hence, an extended elastic behavior, which means tremendous variations in chip thickness and fluctuating cutting forces. Moreover, very low heat conductivity causes the formation of serrated chips, which further increase the fluctuation in cutting forces. The purpose of this work is to study the influence of the tool entering angle on the stability of the process and on tool life based on a time and frequency domain analysis of the cutting forces. The results show that lower entering angles may provide stabler cutting, as indicated by the regular tool wear instead of the microchipping resulting from the use of a higher value of this angle. Although cutting forces are larger at lower entering angles, the tool life is much longer, since most of this load is associated with low frequencies, at which the tool behaves like a rigid body. & 2009 Elsevier Ltd. All rights reserved. Keywords: Machining Milling Vibration Cutting forces Titanium alloys 1. Introduction Although titanium alloys have outstanding mechanical properties such as high hot hardness, good strength-to-weight ratio, and high corrosion resistance, their low thermal conductivity, high chemical affinity to tool materials and low Young modulus severely impair their machinability [1]. First and foremost, titanium alloys are poor heat conductors. Their thermal conductivity is almost 7 W/m K, while that of stainless steels is about 18 W/m K and that of carbon steels is about 50 W/m K [2]. Therefore, the heat generated during machining processes is concentrated mainly at the tool’s cutting edge, causing it to lose hardness and mechanical resistance and leading to its plastic deformation and/or rapid wear [3]. Titanium alloys have chemical affinity for all known tool materials, which, along with high temperatures generated in the cutting zone, provides strong adhesion of workpiece material over the tool edge. Mechanisms of attrition and diffusion can accelerate tool wear and lead to edge breakage [4]. Because of its low Young modulus, the volume of workpiece material in the vicinity of the machined surface undergoes excessive elastic deformation during machining, preventing a  Corresponding author. Tel.: + 55 16 33518513. E-mail addresses: antonialli@ufscar.br (A. Italo Sette Antonialli), anselmo@fem.unicamp.br (A. Eduardo Diniz), robson@fem.unicamp.br (R. Pederiva). 1 Tel.: + 55 19 3521 3292. 0890-6955/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2009.09.006 good finish, particularly in the case of thin walls [5]. In milling or other processes associated with interrupted cutting, a low Young modulus causes major variations in chip thickness, i.e., high vibration levels, especially chattering—or self-excited vibrations— which cause tool edge microchipping and the premature end of its service life [6]. This type of vibration also increases in response to the formation of serrated chips, which is also a consequence of low heat conductivity and further increases fluctuations in cutting forces [7]. The diagram in Fig. 1 illustrates the regenerative effect of chatter vibration on milling, showing the ripple left by the last cutting edge that cut the workpiece and the ripple to be left by the cutting edge currently at work. Tangential and radial components of the cutting force, Ft and Fr, respectively, are functions of forces measured at the x and y axes and the instantaneous angle (j) of the feed direction. The detail in the upper left-hand corner of the figure shows how these ripples left on the workpiece cause intense variations in chip thickness (h), imposing a different load on each tooth at every rotation of the tool. In addition, the ability of titanium alloys to maintain their mechanical properties at high temperatures also hinders their machinability because it interferes in the plastic deformation needed for chip formation [9]. Lastly, thin chips, and therefore brief contact between chip and tool rake face causes high stresses at the cutting edge [10]. The main goal of this work was to devise a way to decrease the vibration of the cutting tool in the milling process of Ti–6Al–4V. To this end, we used tools with very low entering angles (kr) in ARTICLE IN PRESS 66 A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 Fig. 1. Regenerative effect of chatter vibration on milling [8]. Fig. 2. Cutting force directions for different entering angles [12]. order to decrease the radial component of the cutting force (because the tool is less rigid in the radial direction, radial forces bend it) and increase the axial component of the force [11], as shown in Fig. 2. The axial direction is very rigid, because when the tool is pressed in this direction it is pushed against the machine spindle which is very rigid. In addition, we intend to gain an insight into the tool’s radial vibration since a decrease of vibration in this direction, which is not very rigid, reduces the tool’s overall vibration. 2. Material and methods 2.1. Equipment The experiments were performed in a 3-axis CNC vertical machining center with 22 kW of power in the spindle motor and a maximum tool rotation of 12,000 rpm. Before starting the experiments, the cutting tools were subjected to a vibration analysis test, as shown in Fig. 3, using a Brüel & Kjær 4506 piezoelectric accelerometer and an instrumented hammer with a Brüel & Kjær 8200 force transducer in order to identify their transfer function in a broad range of frequencies. Samples were recorded at 20 kHz. A Kistler 9257BA stationary dynamometer, a National Instruments PCI-6025E analogical/digital data acquisition board and LabVIEWs 8.5 software were used for 3-axis cutting force measurements. The signals were processed with Matlab 7.1 software. Cutting forces were measured before starting the tool wear tests, i.e., the tool presented no wear when the forces were measured. Tool wear evolution during the tests was monitored using a Leica stereomicroscope with 50  maximum magnification and ImageJ 1.40c software. The end of tool life (and the end of an experiment) was determined by a maximum flank wear of 0.2 mm. ARTICLE IN PRESS A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 67 Fig. 4. R210 and R300 tools. Fig. 3. Vibration analysis test setup [8]. After concluding the tests, the tools were examined in a scanning electron microscope (SEM) Jeol JXA-840A, which provides higher magnification and has an energy dispersive X-ray spectrometer (EDS) resource that allows chemical elements to be identified, and therefore enables wear mechanisms to be found or at least surmised. 2.2. Materials Tests were performed on a recrystallized plate of Ti–6Al–4V, the most common titanium alloy. Two different milling cutters were used here, both with a maximum diameter of 25 mm, as recommended by tool manufacturers for face milling with high feed, intermittent machining, ramp milling and helical interpolation [12]. The first cutter, manufacturer code R210-025T12-09M, had a 101 entering angle (kr) and two square flat inserts, while the other one, manufacturer code R300-025T12-10M, had three round inserts with chip breakers, so the entering angle varied as a function of the depth of cut. Both types of inserts were coated with a multilayer of TiN/TiAlN by physical vapor deposition (PVD). All this tooling is shown in Fig. 4. All the experiments were carried out using a 10% brix concentration of vegetable-based emulsion applied externally on the tool at a flow rate of 45 l/min. forces. To this end, five experiments were performed, as indicated in Table 1. As this table indicates, both entering angles and other variables changed from one test to another. At first, the tool used in each experiment defined the value of the entering angle: when R210 was employed, kr was necessarily equal to 101; when the R300 tool was used, kr was dependent on the axial depth of cut (ap), as will be shown in Section 3. The cutting speed (vc) and feed per tooth (fz) were varied to maintain a constant overall chip thickness (hm) in all experiments and material removal rate (Q) in the first, fourth and fifth experiments. The purpose of the second experiment was to evaluate the influence of the cutting speed on the output variables, since the only difference between the conditions of the first and second experiments was the cutting speed. Moreover, as can be seen by comparing the second and fifth experiments, the only difference was the entering angle (and of course the material removal rate). The third experiment was carried out with the same entering angle and cutting speed as in the second experiment, but the tool was equipped with round inserts (R300), which required reducing the depth of cut. The decision to maintain a constant overall chip thickness (hm) in all the experiments was based on its influence on the specific cutting pressure (ks). Fixing the material removal rate (Q) in three experiments allowed for a coherent comparison of the experiments in terms of tool life. All the milling tests were performed three times. 3. Theory and calculations When the R300 tool is used, the entering angle (kr) varies as a function of the axial depth of cut (ap), as indicated in Eq. (1) and Fig. 5: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! ap ð1Þ kr ¼ tan1 iC  ap 2.3. Methods where iC is the diameter of the tool insert. The material removal rate (Q, (mm3/min)) is a function of the axial depth of cut (ap, (mm)), radial depth of cut (ae, (mm)), cutting speed (vc, (m/min)), feed per tooth (fz, (mm)), number of tool inserts (z), and the tool effective diameter (De, (mm)), as The purpose of this work was to identify correlations among tool entering angle (kr), tool life, wear mechanisms and cutting   ap ae Vc fz z Q ¼ 1000 pDe ð2Þ ARTICLE IN PRESS A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 68 Table 1 Cutting parameters for each test. Number 1 2 3 4 5 Test Tool kr (1) vc (m/min) ap (mm) fz (mm) hm (mm) Q (mm3/min) R210_10_40 R210_10_50 R300_10_50 R300_10_90 R300_18_50 R210 R210 R300 R300 R300 10 10 10 10 18 40 50 50 90 50 1.0 1.0 0.3 0.3 1.0 0.19 0.19 0.19 0.19 0.10 0.02 0.02 0.02 0.02 0.02 3180 4030 1780 3180 3180 Fig. 5. R210 and R300 tools. The overall chip thickness (hm, (mm)) is calculated by hm ¼ 180 pj0 fz sin kr ð1  cos j0 Þ ð3Þ where j0 [deg.] is the tool–workpiece contact angle. In all the experiments, j0 was kept at 1101, the situation in which the radial depth of cut (ae) is equal to 2/3 of the effective tool diameter (De), as recommended by Diniz et al. [11] to optimize the tool’s entry into the workpiece. Transfer functions (H(o)) acquired in vibration analysis tests are calculated by fXðoÞg ½HðoÞ ¼ fFðoÞg frequencies (whose amplitude is much higher than that of other frequencies) for both tools are above 2000 Hz. However, the detail in the upper left-hand side of the figure shows that, in the frequency range 400–1000 Hz, transfer functions tend to increase above 0.05 m/N s2, which means that tools will not behave like rigid bodies if excitation occurs in those frequencies. In other words, tools will be subjected to a much higher acceleration (and so, to a higher vibration amplitude) if the same force is applied in this frequency band (see Eq. (4)). It can therefore be stated that if the range of frequencies of the cutting forces exceed 400 Hz, tools will undergo some kind of vibration that would not occur in the presence of lower frequencies. This anomalous behavior seems to be a self-excited phenomenon, in which any of the tools’ structural mode, is somehow excited by the input force, regardless of its size [14]. Figs. 7, 8 and 9, respectively, illustrate the behavior of the tangential, radial and axial components of the cutting force in the time domain of 0.2 s in all the tested conditions. Fig. 10 shows the RMS (root mean square) value of these components for each experiment. As indicated in Figs. 7 and 9, the tangential and axial cutting force components varied similarly in the tests, clearly showing that the R210 tool produced greater forces (experiments R210_10_40 and R210_10_50) than the R300 tool (experiments R300_10_50, R300_10_90, R300_18_50). One reason for this is the larger cutting width (b) of the R210 tool, which causes only higher friction between the tool and workpiece, and hence a higher cutting force. The cutting width (b) is a function of both axial depth of cut (ap) and tool entering angle (kr), as indicated in Eq. (6): b¼ ð4Þ where X(o) (m/s2) is the magnitude of the acceleration acquired by the accelerometer and F(o) (N) is the force measured by the force transducer (on the instrumented hammer) [13]. The tangential, radial and axial components of the cutting force on the tool, Ft, Fr and Fa, respectively, are functions of instantaneous angle (j) of the feed direction and can be obtained by 8 9 2 38 9 sin j cos j 0 > > < Ft > < Fx > = = 6 7 F Fr ¼ 4 cos j sen j 0 5 ð5Þ y > > :F > :F > ; ; 0 0 1 z a tool workpiece When the cutting forces were measured while cutting a workpiece fixed onto the dynamometer, the components measured were parallel to the three axes of the machine tool (Fx, Fy and Fz) and, for our purposes, it was interesting to have the Ft, Fr and Fa components. 4. Results and discussion Fig. 6 shows transfer functions for both R210 and R300 tools in the frequency domain, clearly indicating that all the natural ap sin kr ð6Þ Thus, in the R210_10_40 and R210_10_50 tests (both with ap =1 mm), b was close to 6 mm, while in the R300_10_50 and R300_10_90 tests (ap = 0.3 mm), b was equal to 2 mm, and in the R300_18_50 test (ap =1 mm) it was equal to 3 mm. The RMS values for both the tangential and axial cutting force components (Fig. 10) attest to the influence that the cutting width exerts on them, since the values of these components were higher with the R200 tool than with the R300 tool. Differences in the cutting force components between experiments with the same b may be attributed to the cutting speed, since high velocities may reduce friction between the tool and workpiece. Unlike the other components, the radial component scarcely varied in the various tested conditions, as indicated in Figs. 8 and 10. This component was much lower than the tangential and axial components in all the tests, due to the low entering angles applied (either 101 or 181 are much lower than 901, a typical entering angle for end mills). Only the R300_10_50 experiment seemed to produce a slightly higher radial force, which may indicate the intense deformation occurring on the workpiece surface when low depth of cut and cutting speed were employed. As stated earlier herein, this work began starting from the assumption that if the entering angle were increased, it would ARTICLE IN PRESS A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 69 Fig. 6. Transfer functions for R210 and R300 tools. Fig. 7. Tangential component of the cutting force. cause an increase of the radial force (which is the force component that bends the tool), which would lead to higher tool vibration and shorten the tool life. However, the values of the radial components were not affected by the entering angle, so we decided to apply a frequency domain analysis of the signal to check how this force component influences tool vibration. Using a fast Fourier transform algorithm and the Hanning window, it was possible to identify the main frequency bands, to which the radial load is associated. Fig. 11 shows the radial component of the cutting force plotted in the frequency domain. As low cutting speeds were used and, consequently the frequency of tool entry on the cutting was low (always below 77 Hz), most of the radial cutting force component was associated with frequencies below 400 Hz. However, some of the tests presented relevant energy levels (near 2 N) in the frequency range 400–1000 Hz, which were detected by the vibration analysis test (Fig. 6) and identified as an intense vibration frequency band. Based on this result, we proposed a parameter to quantify this part of the radial component of the cutting force by its signal standard integration in the frequency domain between 400 and 1000 Hz, defining the radial load rate associated to this frequency band, F_ rð4001000Þ , as follows in Eq. (7): F_ rð4001000Þ ¼ Z 1000 Fr @o 400 ð7Þ ARTICLE IN PRESS 70 A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 Fig. 8. Radial component of the cutting force. Fig. 9. Axial component of the cutting force. Fig. 12 compares the F_ rð4001000Þ of all the experiments, showing clear differences, i.e., the R300_18_50 test presented the highest radial load rate, followed in decreasing order by R300_10_90, R300_10_50, R210_10_40 and R210_10_50. This figure indicates that both the entering angle and the type of tool influence F_ rð4001000Þ . These quantities are not related to the size of the radial component itself, but they appear to be directly related with the entering angle (the experiment with the highest entering angle caused the highest F_ rð4001000Þ value) and also with the type of tool (the values obtained with the R300 tool were higher than those obtained with the R200 tool even when the same entering angle was used for both tools). It is important to note that the radial load rates of 400–1000 Hz in the R300_10_50 and the R300_10_90 experiments were much higher than when the R210 tool was used (Fig. 12), although in this last experiment a lower depth of cut was employed and, hence, a smaller RMS cutting force was found (Fig. 10). That indicates unequivocally that the R300 tool generates forces at higher frequencies, which may be due to the shape of the chip. The chip produced by the R210 tool occupies an approximately rectangular area on the rake face, while the chip formed by the R300 tool has a comma-like shape (see Fig. 13), ARTICLE IN PRESS A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 71 Fig. 10. RMS values for the cutting force components. Fig. 11. Frequency domain of the radial component of the cutting force. which causes severe friction between the tool and workpiece, since part of the chip always has a thickness equal to zero, regardless of the instantaneous angle of the feed direction (j). This friction may be the cause of the vibration at higher frequencies. Tool life, machined area and volume of material removed per tool life are plotted in Fig. 14. The longest tool life was attained in the tests with kr = 101, except for the R300_10_90 test. This exception may be attributed to the cutting speed (90 m/min), which is very high for titanium alloys. On the other hand, in the experiment with an 181 entering angle (R300_18_50), the tool’s performance was not acceptable. If one compares the tool life of the R210_10_50 and R300_18_50 experiments (the differences between these two experiments were the entering angle and the material removal rate, but the cutting speed was the same), one can see that the tool life in the former was much longer than in ARTICLE IN PRESS 72 A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 Fig. 12. Radial load rate of 400–1000 Hz. Fig. 13. Chip shapes for R210 and R300 tools. that of the latter, even though the former removed more material per minute. Force measurements showed that neither cutting force even its radial component were excessively high in the R300_18_50 (see Fig. 10) condition; however, the radial load rate over 400 Hz was substantially higher with kr =181 than with kr = 101 (see Fig. 12). Of all the conditions tested here, the R300_10_50 test provided the largest machined area. However, the volume it removed per tool life was much lower than that achieved in the R210_10_40 and R210_10_50 tests because of the small depth of cut required to obtain a kr = 101 in this configuration. Nevertheless, this condition can be used in finish milling, when little stock material is to be removed. Finally, Fig. 15 depicts SEM micrographs of the worn edges of the tools (end of tool life) used in each experiment. The effect of the entering angle and chip shape on the wear pattern is visible: the tool used in the R300_18_50 test, the only one with kr = 181, is the only one that clearly showed breakage on the cutting edge. This test presented the highest F_ rð4001000Þ value. The importance of the radial load rate at high frequencies (400– 1000 Hz) was confirmed, since this type of wear is a typical fatigue phenomenon. As mentioned earlier, vibration in this frequency range led to tool fatigue followed by breakage of the cutting edge. The tool-high-vibration phenomenon was absent in the other conditions, which showed the normal wear mechanisms. The smooth flank wear land of the tools used in the R210_10_40 and R210_10_50 tests indicates that diffusion was the main wear mechanism on these tools. It should be kept in mind that titanium has a high chemical affinity for all known tool materials, which facilitates diffusion wear. In addition to the smooth surfaces, these micrographs show several layers of workpiece material (Ti, Al, V) adhering to parts of the wear land, indicating that attrition also contributed to the end of tool life, mainly for the tools used in R300_10_50 and R300_10_90 tests. These tools displayed much rougher wear lands with numerous layers of workpiece material adhering to them, suggesting that the main wear mechanism of these tools was attrition. Trent and Wright [15] state that in the presence of vibration, the metal flow past the tool may be very uneven, causing small fragments of the tool to be removed by attrition. As Fig. 15 shows, the radial load rate of 400–1000 Hz in these two conditions (R300_10_50 and R300_10_90) was not as high as in the R300_18_50 test. Therefore, the vibration was insufficient to cause mechanical fatigue and cutting edge breakage. However, this parameter was higher in these conditions than with the R200 tool, leading to the conclusion that tool vibration led to attrition, which shortened the tool life. 5. Conclusions This paper described a cutting-force-based vibration analysis to ascertain the effect of the tool entering angle on tool vibration and thus on tool life in a titanium alloy milling operation. Tool vibration analysis tests indicate the range of frequencies, in which ARTICLE IN PRESS A. Italo Sette Antonialli et al. / International Journal of Machine Tools & Manufacture 50 (2010) 65–74 73 Fig. 14. Tool life, machined area and volume of removed material. the tool vibration is amplified. In the case of the tools used here, this frequency band was above 400 Hz. The radial component of the cutting force in each experiment was analyzed in the frequency domain, providing a load rate quantified for that range of frequencies (400–1000 Hz). The tool life and wear pattern in all the tested conditions were elucidated and correlated to tool vibration in that frequency range. It was concluded that the use of a tool with a higher entering angle and round inserts associates radial load to higher frequencies, at which the tool does not behave as a rigid body. This led to cutting edge breakage that shortened the tool life. A lower entering angle resulted in normal wear mechanisms of diffusion and attrition. Therefore, a productive milling operation on Ti–6Al–4V alloy and a long tool life require reduced tool vibration. Lower vibration will prevent cutting edge breakage caused by fatigue, after which the problem of reducing tool wear can be tackled. Acknowledgements The authors are indebted to Blaser Swisslube and Embraer for providing the cutting fluid and titanium alloy used in this work, and to Sandvik Coromant for providing tools and financial support. CNPq is acknowledged for granting a scholarship. References Fig. 15. SEM micrographs of the worn edges. [1] K.A. Venugopal, S. Paul, A.B. Chattopadhyay, Growth of tool wear in turning of Ti–6Al–4V alloy under cryogenic cooling, Wear 262 (2007) 1071–1078. [2] S. Lampman, Wrought titanium and titanium alloys, Metals Handbook, vol. 2, ASM International, Materials Park, 1990, pp. 592–633. [3] E.O. Ezugwu, J. Bonney, Y. Yamane, An overview of the machinability of aeroengine alloys, J. Mater. Process. Technol. 134 (2003) 233–253. [4] M. 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