Considerations on Process Performance in Incremental Forming by Inducing High Frequency Vibration D. Mundo, G. Gatti, G. Ambrogio, L. Filice and G. A. Danieli
Abstract The paper is focused on the formability and other specimen characteristics obtained in Single Point Incremental Forming (SPIF) processes. In particular, it is known that friction heavily affects the results because the deformation is very localized at the contact between punch and sheet. Despite the presence of the lubricant, some effects are evident, such as the material wear, the staircase shaping and the geometry torsion. Finally, it is reasonable to think that the effect is also played on the allowable formability and then, like in other metal forming processes, a high frequency oscillation is imposed to the sheet in order to minimize the friction effect. The results are accurately discussed in the paper. Keywords Single Point Incremental Forming · Vibrations · Formability · Friction
Introduction Incremental Forming processes have been recently introduced in the manufacturing scenario and, for this reason, many aspects related to their mechanics are not well explained, despite the relevant effort spent by several researchers all over the world [1–4]. Among the most interesting aspects, formability plays a strategic role since, in this sense, the process efficiency is very high as compared to the traditional stamping processes. In fact, the strain that the sheet can tolerate is higher than in drawing processes. In technical literature, many papers focused on material formability and other relevant issues in Incremental Forming can be recognised, and the role of the main D. Mundo (B) Dipartimento di Meccanica, Universit`a della Calabria, Via P. Bucci, 87036, Arcavacata di Rende (Cs), Italy e-mail:
[email protected]
M. Ceccarelli (ed.), Proceedings of EUCOMES 08, C Springer Science+Business Media B.V. 2009 DOI 10.1007/978-1-4020-8915-2 63,
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process parameters is accurately discussed. Among these parameters, friction represents a key-factor since it is responsible for the sheet wear, especially when a small pitch (i.e. the distance between two sequential coils) is selected. This wear can exalt the local material thinning resulting in an early failure. Furthermore, friction induces a sort of torsion action on the profile that causes a geometrical error on the final obtained geometry. Up to now the friction is reduced as much as possible utilising two ways: the use of punches characterised by a grinded surface and the use of a suitable lubricant, typically mineral oil. In this paper, a strategy for exalting the lubrication action is implemented, according to other researches which applied an analogue technique to other metal forming processes. The logic is based on the reduction of friction that automatically results in an increasing formability or, anyway, in the improvement of process robustness. In particular, an experimental equipment was set up with the aim to generate high frequency vibrations into the sheet. This method allows the cyclic instantaneous detachment between sheet and tool which induces two immediate advantages: the relaxation of the axial induced stress and the lubricant inflow between working material and tool. A commercially pure Aluminium Alloy (AA1050) sheet, 0.5 mm thick, was used as raw material. The vibration has been generated using a proper resonator, connected to the sheet, and driven by a wide spectrum function generator. The main results are discussed in the follow.
Remarks on the SPIF Process Single Point Incremental Forming is characterized by a peculiar process mechanics which makes such technology very far from conventional sheet metal stamping. Here, in fact, plastic strain is accumulated through the progressive and incremental application of localized deformations at the interface punch-blank. Several studies were performed with emphasis on assessing and improving the formability in this forming method [5], Iseki and Kumon [6] performed the incremental stretching test for various materials and found that the FLCs are approximately linear. Kim and Park [5] proposed the double-forming technique to improve formability, assuming that only shear deformation occurs in the material. Shim and Park [7] performed a series of experiments and suggested the straight grove test as a method to asses the formability for annealed Aluminum sheet. In addition to these results, subsequently, Kim and Park [8] observed that formability differs according to the direction of the tool movement. It’s quite evident that the total amount of deformation depends on the draw angle ␣ (Fig. 1), but it is achieved through the “sum” of small localized deformations. The latter, in turn, depends on the size of the step down ⌬z, between two subsequent loops of the tool. It’s obvious that the values of the step down ⌬z and of the step inward ⌬x must be combined in such a way to ensure the desired slope, but the size of ⌬z actually determines the value of the localized deformation applied at each step.
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Fig. 1 Single Point Incremental Forming base dimension sketch
At the same time, a relevant role is also played by the process parameters, such as the tool diameter of the tool depth step, utilised during the process, and the friction conditions, due to the continuous sliding on the 3D trajectory. More in detail, on this second topic is focalised the study carried out, aimed to find newer solution to improve the process efficiency reducing the friction negative effects.
The Experimental Work An experimental rig was set up in order to support the sheet metal blank properly and induce vibrations into it during the SPIF process. Harmonic excitation is induced by means of a permanent magnet shaker connected to the sheet using a steel stinger. This allows for in-plane oscillating components to be reduced, so that investigation of out-of-plane vibrations only may be performed [9]. Previous experimental tests showed that, far away from the manufacturing region, material slide during SPIF is negligible and this allows for the vibrating system to be just laid down on the machine base. In order to select the point of application of the harmonic force excitation and its frequency, numerical simulations are preliminarily carried out on the sheet metal blank.
Numerical Simulations Numerical simulations were preformed in order to estimate the mode-shapes of vibration and the corresponding natural frequencies [10] in the plastic-undeformed sheet. The FE software Msc-Nastran was used for computation of the structural vibrations. The real eigenvalue analysis was obtained by Nastran solution sequence SOL103. The boundary conditions for the plate are specified as clamped edges [11] and the following geometrical and material properties were used for simulation: plate dimensions 200×200×0.5 mm2 , Young’s modulus Y=70 kN/mm2 , Poisson’s
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ratio ν=0.33, mass density ρ=2700 kg/m3 . First, second, forth and fifth mode-shape are shown as fringe contour plots in Fig 2a– 2d. and corresponding natural frequencies are also indicated. Second and third mode-shape are rotated 90◦ with respect to each other. Figure 2b shows, in fact, results for the second mode only. Due to plate symmetry, natural frequencies for these two latter modes coincide. In Fig. 2a–2d, white zones indicate a null out-of-plane displacement, which corresponds to either a clamped boundary region or a nodal line for the actual mode of vibration. If the point of excitation is placed at a nodal line, the corresponding mode of vibration is not excited. Besides, if the plate vibrates according to a single mode, no out-of-plane displacement occurs on the corresponding nodal lines. From the above consideration, it follows that the exciting frequency could be properly selected by focusing on the shape of the vibration mode related to the shape of the final manufactured part. Mode 1 (Fig. 2a) is axially symmetric, which means that, if the excitation frequency is tuned to the first natural frequency, points laying on a circle centred on the plate will all vibrate harmonically in-phase with the same amplitude. No nodal lines exist for this mode. Exciting the sheet metal blank at that frequency could thus be effective when manufacturing axially symmetric parts. However, most of the energy supplied to the plate by the auxiliary vibrating system will be lost in the most inner region of it, partially effecting the manufacturing process. On the other hand, mode 5 (Fig. 2d) is characterized by two nodal lines along the plate’s diagonals. Maximum energy is located approximately at 0.2L from each
Fig. 2 Mode-shapes and corresponding natural frequencies for the plate
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edge, L being the dimension of the plate sides. This could be possibly effective when forming squared-section products with vertices on the nodal lines. Nevertheless, the following consideration are possible. Natural frequencies, as theoretically calculated, are largely affected by the actual structure’s boundary conditions, which may be different from the ideal constraints assumed earlier for simulation. Furthermore, the auxiliary wooden die (baking plate), could also affects those results. Mode-shapes are, conversely, only partially affected by boundary conditions’ changes, especially at lower frequencies. It is also worth to notice that results shown in Fig. 2 refer to the sheet metal blank in its plastic-undeformed condition. This means that, as plastic deformation occurs and the product starts forming, mode-shapes and frequencies change. These effects could be investigated in future works.
Experimental Rig All the experiments were executed keeping fixed some process parameters (Dp =18 mm, p=0.3 mm and thickness s=0.5 mm and tool rotation speed s=120 r.p.m.) and two pairs of experimental test were planned as follows. In the first pair, the metal sheet was excited at its first natural frequency, while in the second the fifth natural frequency was used. In each pair of test, a rounded-section and a squared-section part are manufactured. Following the discussion in the previous section and with reference to Fig. 2, the point of excitation is selected to be at 0.5L from the lower edge and at 0.2L from the right one. In this configuration either the first or the fifth mode can be effectively excited. A hole is drilled through the baking plate to allow the connection of the shaker stinger to the metal sheet. A suitable supporting frame was manufactured as shown in the Figs. 3 and 4. A permanent magnet vibration shaker (LDS V201/3) was used to excite the metal
Fig. 3 Experimental rig
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Blank-holder
Tool
Auxiliary wooden die
Metal sheet
Stinger
Frame Shaker
Fig. 4 Sketch of the experimental rig (vertical section)
sheet through a 15 mm steel stinger placed on its bottom side. Armature resonance frequency of the shaker is 13 kHz and nominal power is 48 W. The signal from a frequency generator is then fed to the shaker through a power amplifier unit.
Experimental Validation In order to tune the excitation frequency of the shaker to the actual resonance frequency of the sheet, an experiment was conducted to measure its actual vibrational response. The sheet metal blank was mounted in place and fixed by the blank-holder. A modal test was performed using a frequency analyzer (LMS Scadas III), an instrumented impulse hammer (PCB 086C03) and a ceramic shear ICP accelerometer (PCB 333B32). A bandwidth of 1 kHz with 1024 spectral lines was selected for acquisition. With reference to Fig. 2, the response of the plate was measured at point located at 0.2L from the left edge and 0.5Lfrom the lower, while it is excited at a point symmetric to the former. LMS TestLab software was used for signal acquisition and processing. A 5-averaged frequency response function is calculated and the first and fifth resonance frequency of the actual plate are estimated to be 200 Hz and 680 Hz respectively.
Results and Discussion The two pairs of tests described in Section Experimental Rig were performed. Experimental results qualitatively confirm the expectations. Formability limit can be effectively represented by the maximum slope angle. In the investigated case, in normal conditions, it is more or less 65◦ , using the given parameters. Formability increasing is slightly shown even if its amount is limited to about 2.5◦ . In terms of thinning the increasing is a bit less than 10%, as summarized in Table 1. At the same time, a better surface roughness was obtained, mainly due to the reduction of the wear phenomenon.
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Table 1 Performance of the SPIF process with and without vibrations Without vibration Maximum slope Thinning Torsion effect
Up to 65 58% Evident
◦
With Vibration Up to 67.5◦ 62% Less evident
Finally, a substantial reduction of the torsion effect due to the torque applied to the specimen by the punch, during the process, was observed. The latter constitutes a good news in term of dimensional accuracy. Results are promising and suggest that further investigation could be part of future developments even if the effects are less evident respect to other processes in which the contact surfaces are larger. In order to overcame the limitation highlighted in Section Numerical Simulations, adaptive feedforward and feedback control of vibration could be used to tune the forcing amplitude and frequency in real-time as the manufacturing process develops. Such a control strategy will possibly improve the whole SPIF process further.
Conclusions Single Point Incremental Forming processes are heavily affected by the friction at the interface between the forming punch and the sheet. The use of simple lubricant (usually mineral oil), substantially reduces these effects but some consequences remain. The strategy discussed in this study, based on inducing a high frequency oscillation into the sheet, supplies interesting results if some critical issues are considered. In detail, it is possible to summarize the following issues: – formability slightly increases thanks to the reduction of the localized wear and stress induced by the punch action on the sheet; – the surface quality is higher as compared to the one obtained in the conventional process; – the distortion effect on the geometry due to the torsion of the specimen is less evident. For above reasons, it is possible to state that although more efforts have to be spent in that direction, the use of the proposed strategy seems very promising to improve the overall performance of SPIF process. Acknowledgments This work was funded by Italian Ministry for Education, University and Scientific Research (M.I.U.R.). The authors would like to thank EP Francesco Pulice for his support during experimental equipment development.
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