Finite element simulation of ultrasonically-assisted turning of a Ti-based alloy M. Demiral1, A. Roy and V. V. Silberschmidt
Abstract Many modern engineering materials are very difficult to process with conventional machining methods. Ultrasonically assisted turning (UAT) is an advanced technology, where high frequency vibration (frequency f≈20 kHz, amplitude a≈15 µm) is superimposed on the movement of the cutting tool. Compared to conventional turning (CT), UAT allows significant improvements in processing many intractable materials, such as high-strength aerospace alloys and composites, by producing a noticeable decrease in cutting forces and a superior surface finish. Vibro-impact interaction between the tool and workpiece in UAT during the chip formation leads to a dynamically changing cutting force in the process zone as compared to the quasistatic one in CT. The paper presents computational (finite-element) model of both CT and UAT. Stresses in the workpiece and forces acting on the cutting tool are studied. Keywords: Ultrasonically assisted cutting, Finite elements, Mechanics of cutting, Machining 1.
Introduction
Ultrasonically-assisted turning (UAT) is an advanced machining technique, where high frequency vibration with an amplitude of 10-20 µm is superimposed on the movement of a cutting tool (Fig. 1). Compared to conventional turning (CT), this technique allows for significant improvements in processing intractable materials, such as high-strength aerospace alloys, composites and ceramics and can be also used in cutting bone tissues.
Figure 1: Principal vibration directions during ultrasonically-assisted turning. 1
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The use of superimposed ultrasonic vibration in a turning process demonstrates improved mechanics of material separation processes, yielding significant decreases in cutting forces, as well as a superior surface finish [Ahmed, Babitsky and Silberschmidt (2006, 2007, 2009)]. The cutting force is one of the governing parameters defining efficiency of the cutting process. A reduction in the cutting force would result in the extension of the tool life, reduced imposed and hence residual stresses in the workpiece, as well as improved surface finish and roundness of machined workpiece. A titanium-based betaalloy (Ti15V3Cr3Al3Sn) is used as a material of the workpiece. Such alloys are used in the aerospace and other advanced engineering fields because of their high strength and toughness, light weight, extraordinary corrosion resistance, and ability to withstand extreme temperatures. As a preliminary study of this newly developed alloy, the simulation for the workpiece material INCONEL 718 was carried out in Ref. [Demiral, Ahmed, Roy and Silberschmidt (2010)]. The chip formation process in ultrasonically-assisted turning (UAT) involves several physical processes such as large plastic deformation of the material inside the chip (which may be of the order of several hundred percent), friction of the chip and workpiece with tool at the rake and free face, respectively, complex interaction between the workpiece-chip-tool system itself [Astashev and Babitsky (1998)]. In order to gain a better understanding of the thermomechanics of this advanced machining technique, a simplification of some complicating features in cutting is necessary for a better understanding of underpinning deformational mechanisms. That leads us to consider the dynamic indentation process with a predefined indenter velocity as a process incorporating the main features of the real turning process but avoiding, e.g., effects due to its complex kinematics. The results of the study can be found in Ref. [Demiral, Roy and Silberschmidt (2010)-1]. 2.
Finite-element modelling of UAT
The three-dimensional thermomechanically coupled FE model is based on the MSC.Marc general FE code [MSC, Marc User’s Guide (2005)]. Figure 2 shows a scheme of relative movements of the workpiece and cutting tool in orthogonal 3D simulations of UAT: the feed direction is vertical, thus the uncut chip thickness, t1, corresponds to the feed rate (t1 = 0.1 mm was used in simulations). The dimensions of a part of the workpiece used in simulations are 6 mm in length and 1 mm in height with the depth of cut (or cutting edge engagement length) d = 0.4 mm. The simulated cutting speed is 150 mm/s. The cutting is simulated from the moment of initial engagement between the tool and the workpiece till the steady state, characterized by the saturation level temperatures and non-changing deformation patterns.
Figure 2: A scheme of the relative movement of the workpiece and cutting tool in
3D simulations of UAT. The relative movement of the workpiece and cutting tool in CT is simulated by the translation of the tool with the constant velocity. Harmonic ultrasonic vibration with a vibration amplitude of 16 µm (peak-to-valley) and frequency value of 18 kHz is then superimposed on this tool movement in the tangential direction (i.e. along X-axis in Fig. 2) in order to model UAT. The vibration speed is several times greater than the chosen translational speed of the tool leading to the periodic separation of the tool from the newly formed chip, thus transforming the process of cutting into one with a multipleimpact interaction between the tool and chip. Various stages of such vibration cycle are described in detail in Ref. [Babitsky, Mitrofanov and Silberschmidt (2004)]. The current FE model is fully thermomechanically coupled in order to properly reflect the interplay between thermal and mechanical processes in the cutting zone: excessive plastic deformation and friction at the tool–chip interface lead to high temperatures generated in cutting region, which results in thermal expansion/stresses and also affect material properties of the workpiece, such as thermal conductivity and specific heat. The detailed description of the thermomechanical processes in UAT in comparison to CT can be found in Ref. [Mitrofanov, Babitsky and Silberschmidt (2004)]. The current model enables us to study the influence of vibration parameters (i.e. frequency and amplitude) on the process variables (e.g. stresses, strains, temperatures and cutting forces). The effect of various vibration directions of the tool on the cutting process can also be analyzed. An obvious advantage of the 3D finite-element model is its capability to study various combinations of vibration directions, whereas their experimental implementation can be extremely laborious, as it may require new types of ultrasonic transducers and mounting systems to be designed. Furthermore, the 3D FE
formulation helps one to perform a direct comparison of numerical results with experimental tests for oblique cutting, without requiring any changes to a standard cutting setup. The model also allows for oblique chip formation and chip's expansion in the lateral dimension (along Z-axis in Fig. 2). The preliminary study about the effects of tool geometry on the deformation process in the scope of indentation was carried out in Ref. [Demiral, Roy and Silberschmidt (2010)-2]. 2.1.
Material model
In our study, a Ti-based superalloy (Ti15V3Cr3Al3Sn) is chosen as the material for the workpiece. In order to obtain a stress-strain behaviour of this alloy under various strain rates ( ε ) and temperatures, a split-Hopkinson test [Li and Lambros (1999)] was carried out at Tampere University, Finland. The specimen used in the test was 8 mm in diameter and 8 mm in length. Figure 3 shows the material response of the alloy for different strain rates obtained in the test. The material properties of the alloy are E=87 GPa, ν=0.3, ρ=4900 kg/m3, where E, ν and ρ are the Young’s modulus, Poisson's ratio and density of the material, respectively. Experimental results characterizing the temperature-dependent thermal expansion coefficient [Material property data (2010)] and specific heat value of the workpiece material (CP) used in the simulations are shown in Figures 4 and 5, respectively. Specific heat has been measured in the temperature range between room temperature and 1200°C by means of differential scanning calorimetry (Netzsch DSC 404) calibrated by a sapphire standard [Blumm and Kaisersberger (2001)]. The conductivity of Ti alloy is k=8.08 W/m.K. The nonlinear strain-rate and temperaturesensitive material model used in our numerical simulations consists of sixteen different stress-strain curves obtained for a combination of four different strain rates ( ε =0.1 s-1, 1 s-1, 3331 s-1, 1010 s-1) and four different temperature values (20°C, 600°C, 800°C, 940°C). These curves are modified in such a way that the magnitude of stress values for high strain values are limited by the ultimate dynamic tensile stress (UTS) [Ng, El-Wardany, Dumitrescu and Elbestawi (2002), Maudlin and Stout (1996)] (Figs. 6, 7). As the highest strain rate obtained from the Split-Hopkinson tests ε =3331 s-1 was the stress-strain data for very large strain rate value ( ε =1010 s-1) was taken with a 20% offset from the corresponding values for ε =3331 s-1 (Fig. 6). The used material model is discussed in Ref. [Demiral, Roy and Silberschmidt (2010)-2].
Figure 3: Stress-strain diagrams of Ti15V3Cr3Al3Sn obtained from split-Hopkinson test for different strain rates at room temperature (20°C).
Figure 4: Thermal expansion coefficient of Ti15V3Cr3Al3Sn for different temperatures.
Figure 5: Specific heat of Ti15V3Cr3Al3Sn obtained from differential scanning calorimetry (Netzsch DSC 404).
Figure 6: Modified strainrate-sensitive material model for 20°C.
Figure 7: Modified temperature-sensitive material model for ε =3331 s-1. 2.2.
Friction model
The classical Coulomb model, with the friction force being a linear function of normal force can predict unrealistically high forces at the tool-workpiece interfaces [Mitrofanov, Ahmed, Babitsky and Silberschmidt (2005)] and hence not used in our model. On the other hand, the shear friction model, in which the friction force depends on a fraction of the equivalent stress of the material, is known to better represent the friction process and thus adopted in our study. The friction stress σ fr is introduced in the following form [MSC, Marc User’s Guide (2008)]:
σ fr ≤ -µ
ν σ 2 sgn(ν r )arctan( r ) , νc 3π
where σ is the equivalent stress, νr is a relative sliding velocity, νc is a critical sliding velocity below which sticking is simulated, µ is a friction coefficient, and sgn(•) gives the sign of the argument •. Two different values of the friction coefficients - µ=0.0 and µ=0.5 - are used in the simulations. Needless to say, µ=0.0 accounts for the idealized frictionless condition, considered as an extreme case of friction reduction due to perfect lubrication, and µ=0.5 accounts for a case of high friction, e.g., due to a lack of lubrication (dry condition). 3.
Numerical results and discussion
In this section the numerical results of simulations are evaluated in terms of stress distribution and cutting force to compare and contrast CT and UAT effectively.
3.1.
Stress distribution and cutting force
Differences between conventional and ultrasonic turning in stress distributions in the process zone and contact conditions at the tool/chip interface were investigated. In conventional turning the cutting tools stayed in permanent contact with the chip throughout the entire cutting process. In contrast, in ultrasonic turning the cutter remained in contact with the chip only about 60% of the time (according to FE simulations). Since the cutting tool is in a permanent contact with the workpiece during CT simulations, a practically non-changing stress distribution is present in the cutting tool and workpiece (Fig. 8(a)), while in UAT the stresses attain levels somewhat higher than the stresses in CT when the tool reaches the maximum penetration depth (Fig. 8(b)) and at the withdrawal of the tool, the stress levels in the workpiece drop to the level which is lower than the CT (Fig. 8(c)). Simulations enable us to compare the average forces acting on the cutting tool during turning. The results of simulations showed a significant difference in forces acting on the cutting tool for CT and UAT. Non-changing force is present in the cutting tool for the case of CT because of the permanent contact between workpiece and tool, while in UAT in a single cycle of vibration from the moment of the first contact with the chip, the forces start increasing with penetration and attain a level higher than the average force in CT when the tool reaches the maximum penetration depth (Fig. 9). The force magnitude then starts declining at the unloading stage until it vanishes when the cutter separates from the chip and starts moving away from it. Results prove the reductions in cutting forces by the introduction of UAT. Namely, a drop in average cutting force of 55 % is observed for transformation of turning mode from CT to UAT (Fig. 9). In all the FE simulations conducted for the turning process, the friction condition defined between the cutting tool and the workpiece greatly influence the predictions. The right definition of contact and friction condition at the tool-workpiece interface helps simulate the lubrication conditions. Different lubrication conditions are implemented in the simulations by varying the friction values at the interaction zones between the tool and workpiece. Simulations were conducted to find the effect of friction on the forces in the cutting tool using different models of UAT. A significant difference was observed in forces in the cutting tool when the friction value was increased from µ = 0 (frictionless condition) to µ = 0.5 (Fig. 10). The maximum magnitude of cutting forces is reached when the tool is in full contact with the chip, i.e. at the positive peak of amplitude of the vibration cycle, and these forces start dropping to zero levels when the tool disengages with the chip i.e. starts moving away from the workpiece. The maximum magnitude of cutting forces in simulations with friction is by 20-25% higher than that in frictionless simulation (Fig. 10).
(a)
(b)
(c)
Figure 8: Distribution of equivalent (von Mises) stresses in CT (a) and UAT at different moments of a single cycle of vibration: tool in full contact with the chip (b), tool moves away from the chip (c).
Figure 9: Comparison of force acting on the cutting tool in the cutting direction for CT and UAT simulations.
Figure 10: Comparison of force acting on the cutting tool for UAT in the cutting direction with friction (µ=0.5) and without friction (µ=0.0). 4.
Conclusion
The use of the 3D thermo mechanically coupled model allowed for the study of 3D chip formation as well as predicting distributions of stresses, strains, cutting forces and temperatures in the workpiece and cutting tool. The cutting forces in ultrasonically assisted turning (UAT) are analysed with numerically, with conventional turning (CT) being a basis of comparative analysis. For the typical
combination of vibration parameters (f=18 kHz, a=16 µm) the calculated cutting force in UAT is 45% of that in CT. Apart from these in CT, a non-changing stress distribution
is present in the cutting tool and workpiece because of a permanent contact between them, while in UAT the stresses attain different levels of magnitude depending on the relative position of tool and workpiece. The comparison of simulations with and without friction, corresponding to dry and lubricated turning conditions, respectively, shows that in the latter case the cutting force is by 20–25% lower than the former case in UAT. Acknowledgements Authors would like to acknowledge Tõnu Leemet from Tampere University of Technology and Carsten Siemers from University of Technology Braunschweig for providing the material data for the Ti-based alloy. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. PITN-GA-2008-211536, project MaMiNa. References Ahmed, N.; Mitrofanov, A. V.; Babitsky, V. I.; Silberschmidt, V. V. (2006): Analysis of material response to ultrasonic vibration loading in turning Inconel 718. Mater. Sci. Eng., vol. 424, pp. 318-325. Ahmed, N.; Mitrofanov, A. V.; Babitsky, V. I.; Silberschmidt, V. V. (2007): Analysis of forces in ultrasonically assisted turning. J. Sound Vibrat. , vol. 308, pp. 845-854. Ahmed, N.; Mitrofanov, A. V.; Babitsky, V. I.; Silberschmidt, V. V. (2007): 3D finite element analysis of ultrasonically assisted turning. Comput. Mater. Sci., vol. 39, pp. 149154. Ahmed, N.; Mitrofanov, A. V.; Babitsky, V. I.; Silberschmidt, V. V. (2009): Enhanced finite element model of ultrasonically assisted turning. Int. J. Machining Machinability Mater., vol. 6, pp. 159-173. Astashev, V. K.; Babitsky, V. I. (1998): Ultrasonic cutting as a non-linear (vibroimpact) process. Ultrasonics, vol. 36, pp. 89–96. Babitsky, V. I.; Kalashnikov, A.; Meadows, A.; Wijesundara, A. (2003): Ultrasonically assisted turning of aviation materials. J. Mater. Process. Technol., vol. 132, pp. 157–167. Babitsky, V. I.; Mitrofanov, A. V.; Silberschmidt, V. V. (2004): Ultrasonically assisted turning of aviation materials: simulations and experimental study. Ultrasonics, vol. 42, pp. 81–86. Blumm, J.; Kaisersberger, E. (2001): Accurate Measurement of Transformation Energetics and Specific Heat by DSC in the High-temperature Region. J. Ther. Anal. Calor., vol. 64, pp. 385-391. Demiral, M.; Ahmed, N.; Roy A.; Silberschmidt, V. V. (2010): Mechanics of Material Removal Process in Ultrasonically Assisted cutting: Advanced Finite Element Study.
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