- Email: [email protected]
Interdisciplinary modelling of the electrochemical machining process for engine blades
G Model
CIRP-1338; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Interdisciplinary modelling of the electrochemical machining process for engine blades F. Klocke (1), M. Zeis *, A. Klink Laboratory for Machine Tools and Production Engineering WZL, RWTH Aachen University, Steinbachstr. 19, 52074 Aachen, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Electrochemical machining (ECM) Modelling Engine blade
In this paper an interdisciplinary simulation model of the electrochemical machining (ECM) process for aero engine blades is set up. Simulation results of a compressor vane are presented and compared to optical measurements of actual manufactured workpieces. The simulation model is based on conservation equations for the electric field, fluid flow and heat transfer in combination with analytical functions for the influence of temperature and gas evolution on the specific electrical conductivity. Validation is done by optical in situ measurements. Finally construction rules for an inverse modelling approach are examined and simulation results of the calculated cathode geometry are presented. ß 2015 CIRP.
1. Introduction The major advantages of electrochemical machining (ECM) are its process specific characteristics of high material removal rate in combination with almost no tool wear and no thermally or mechanically damaged workpiece rim zones. Because of cost intensive tool pre-developing processes and rather high investment outlays for the machine tools, however, ECM is specifically used in large batch size production [1]. Due to these aspects ECM represents an important alternative manufacturing technology for turbomachinery components. The current development to increase propulsive efficiency by higherpressure ratio as well as through higher temperature combustion (need for high temperature resistant materials) requires an efficient machining of new designs and advanced materials. Conventional milling nowadays reaches its technological and economical limits especially for the adequate processing of selected difficult-to-cut Nibased alloys [2,3]. Thus, ECM gains more and more importance for the machining of appropriate aero engine blade geometries in serial production. ECM additionally allows the direct production of finishing surface qualities even during rough machining operations, which eliminates the need for further treatment like cost-intensive finish milling steps or grinding and polishing operations [2]. Main reason for high tool costs during ECM is an only knowledge-based, iterative cathode designing process. After a test run the produced workpiece has to be measured and the difference between target and actual geometry due to locally changed electrolysis conditions is subtracted from the cathode and so forth. On the other hand the theoretic background of all physical aspects involved during ECM is very well known, but up to now no comprehensive and interdisciplinary modelling approach is available for the precise simulation of the ECM process for
* Corresponding author. Tel.: +49 241 8027467; fax: +49 241 8022293. E-mail address: [email protected] (M. Zeis).
turbomachinery components and especially blade geometries [2]. First models describing the material removal along the electrolyte flow path in general were developed based on experimental results of standardized tests for different materials, see [4]. Kubeth for example described the basics on the reproduction of the tool electrode geometry and Pahl focused on the achievable geometrical precision [5,6]. Further research e.g. by De Silva et al. focused on the influence of electrolyte concentration on process performance [7], or the modelling of temperature aspects by Deconinck [8]. A first so-called ‘‘Multiphysics Approach’’ for the simulation of ECM processes was presented by Van Tijum et al. [9]. Current research focuses on the study of gap phenomena using transparent electrodes [10] and highspeed camera systems [11,12]. Also process analysis and modelling activities for ECM micro machining [13], electrolyte jet machining [14,15] and Laser-assisted (Jet-) ECM [16,17] are taking place. A recent advanced overview on all ECM simulation approaches is given in [18]. Further details regarding machining of turbomachinery components and hybrid approaches are given in [1,19]. For macro ECM processes temperature and gas evolution affect the conductivity of the electrolyte along the flow path significantly and thus lead to local deviations in dissolving rates [12], Fig. 1. The
Fig. 1. Fluid-dependent material removal during ECM, [12].
http://dx.doi.org/10.1016/j.cirp.2015.04.071 0007-8506/ß 2015 CIRP.
Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071
G Model
CIRP-1338; No. of Pages 4 2
F. Klocke et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
formation of a non-equidistant working gap has therefore especially to be taken into account for the modelling of ECM blade manufacture. In this paper an interdisciplinary simulation model of the ECM process for aero engine blades is set up. Simulation results of a compressor vane are presented and compared to optical measurements of actual manufactured workpieces. The simulation model is based on conservation equations for the electric field, fluid flow and heat transfer in combination with analytical functions for the influence of temperature and gas evolution on the specific electrical conductivity. Validation is done by optical in situ measurements. Finally, construction rules for an inverse modelling approach are examined and simulation results of the calculated cathode geometry are presented.
the experimental results. Furthermore the amount of gas at the end of the electrolyte gap was measured and showed good accordance to the calculated volume, cf. [12]. A comparison of simulated heat-transfer based on Joule heating and according thermography camera recordings is shown in Fig. 3. As the emissivity is unknown, no quantitative values can be given. The qualitative images show a good accordance. The temperature development along the electrolyte channel shows constantly increasing values (horizontal profile) and relatively lower values in areas with high flow (vertical profiles). Caused by anode and cathode materials different heat conductions – shown both in simulation and experiment – are taking place, cf. [12].
2. Interdisciplinary modelling approach Basis of the interdisciplinary model – which is described in detail in [12] – is the description of the anodic metal dissolution by Faraday’s law. The first extension is the electric field, which is modelled by the Maxwell equations. As the electrical properties of the electrolyte are changing along the working gap, it is necessary to model these changes with the Navier–Stokes equations and the energy conservation equation. With this set of conservation equations it is possible to compute a laminar flow effectively. But because the fluid flow can become turbulent in the working gap, a turbulence model has to be added. For the turbulent flow in an electrolyte channel under typical macro ECM process conditions for blade applications the k–e-model describes the behaviour the best. In most former models the electrochemical gas evolution at the electrodes was not considered. But due to the high volume fraction of gas in electrolyte during ECM it is necessary to model the evolution and transport of that gas as well as its influence on the electrical conductivity. For numerical reasons only hydrogen as the major gas during ECM is modelled [12]. Gas evolution itself – as an essential step for building up a simulation model of the macroscopic ECM-process – can be described by the Butler–Volmer equation as a function of the local state variables pressure and temperature. Once evolved at the cathode the hydrogen and the electrolyte form a two-phase flow which is most effectively simulated as bubbly-flow. The influence of the non-conductive hydrogen on the electrical conductivity k of the electrolyte is approximated best by using the Bruggemann equation, cf. [20]. As the fluid simulation is now strongly coupled to the electric field and the temperature, these aspects have to be computed simultaneously in a first step. The material removal is calculated afterwards – due to the need for numerical stability and efficiency – in a second step with the state variables as an input from the first step, cf. [20]. The new modelling approach for gas and temperature evolution was validated by an alignment between simulation results and according optical in situ measurements. Fig. 2 shows that the boundary layer of the bubbly-flow in the simulation grows in the same way compared to the region with high gas content from
Fig. 3. Comparison of thermography camera recordings (a) and heat-transfer simulation (b), based on [12].
Fig. 4 shows a comparison of simulation results for the ECM machining of reference geometry to verify the performance of the new interdisciplinary model. It can be seen that the simulation is in a very good accordance to the experimental results [12] and much better than the industrially established cos(w)-simulation [18]. In contrast to former simulations also the downstream area in the side gap of the outlet shows no deviation, cf. [1,21].
z Inlow
x
Feed rate
Outlow
Exp. Cos(φ)
2 mm
Sim.
Fig. 4. Comparison of simulation results (standard cosine and interdisciplinary approach with consideration of gas and temperature evolution) and experiment for machining simplified macro geometry.
3. Simulation of the removal process of engine blades
Fig. 2. Validation of gas evolution simulation (a) via high-speed camera recordings (b), based on [12].
As a specific application example the simulation model is applied to the guide vane of a multistage axial compressor. The actual production of the analyzed compressor vane was made by the industrial partner Leistritz GmbH (LTT). For this purpose, first the volume of the shear blank from Inconel 718 is redistributed over a full-forward cross-flow process into a preform. In the following rough-forging process the initial geometric contour for the electrochemical sinking is then created. For the sake of clarity in Fig. 5 the intermediate steps waterjet cutting of the excess material and pre-milling of the blade root and head have been omitted. After the ECM process, where the blade surfaces with leading and trailing edge and the annulus collectors are manufactured in one operation, finally blade root and head would
Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071
G Model
CIRP-1338; No. of Pages 4 F. Klocke et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
3
Fig. 5. Demonstration blade and manufacturing process chain. Fig. 7. Phenomena at the trailing edge towards the end of sinking.
be finished by profile grinding completing the whole process chain. The compressor guide vane has tolerances of 50 mm on the blade surfaces and 80 mm on leading and trailing edge. In anticipation of the presented simulation results it should be noted at this point that the simulation relates to the third cycle of geometric cathode tool design done by the industrial partner LTT based on the cos(w)-method (cf. Fig. 4). The flushing direction of the electrolyte was realized in the opposite direction of the aerodynamic flow direction from trailing to leading edge which generated better machining results. Nevertheless, generally still significant deviations between the machined blade contour and the nominal data occurred, Fig. 6. While the blade surfaces are already mapped precisely, at both edges still strong differences from the target geometry given from design can be seen, cf. [22]. Maximum deviations at the leading edge are 83 mm (left detail) and in the flattened area at the suction side of the trailing edge about 81 mm (right detail). For the sake of clarity these values are not shown in Fig. 6 as well as due to the fact that the differences between simulation results and measured machined surface are in the focus.
However, in addition to the purely geometrical comparison, the simulation also opens the possibility to better understand certain results of the mapping process to thereby adjust the process based on knowledge. As one representative example, the influence of different physical effects on the blade trailing edge and thus the inlet side of the electrolyte are discussed, Fig. 7. Due to the sharp edges of the cathode geometry on the downstream side above and below the main flow a dead water region develops. On the one hand here locally process heat accumulates and provides an increased electrical conductivity. On the other hand this effect leads in this area to an increased accumulation of hydrogen gas, which results in a reduction of conductivity. The main flow is deflected upon the trailing edge and accelerated, so that the static pressure decreases. According to the ideal gas law this effect leads locally to an expansion of the hydrogen gas, whereby the gas volume fraction also increases. Further, in Fig. 7 it can be seen that the suction side flow is accelerated slightly faster than on the pressure side, resulting as described in the field of higher gas volume fraction. Due to the geometric conditions, however, the pressure side recirculation region develops slightly larger, so that the influence of temperature predominates in this region. These effects lead to the fact that gas and temperature influence – related to the conductance – are roughly balanced on inlet suction side, while on the pressure side due to temperature a higher conductivity prevails. In total, these conditions result in the fact that the blade trailing edge receives a flattening on the pressure side, while the replication accuracy on the suction side is within the tolerances, cf. [22]. 4. Cathode design for the manufacture of engine blades
Fig. 6. Comparison of simulation and machined geometry with some representative absolute values of the difference between both geometries.
In the global view of Fig. 6 a good accordance between the simulation results and the actual manufactured blade can be seen. The absolute value of maximum deviation on the blade surfaces is about 15 mm, and is well within the specified tolerance band of 50 mm. In the area of the blade leading edge (left detail), the calculated geometry shows a very similar curvature to the machined blade. But in this area the largest deviation of 21 mm occurred, which corresponds simultaneously to the overall highest difference. The blade trailing edge could be calculated very precisely with a maximum deviation of only 11 mm. Summarized it can be stated that the interdisciplinary simulation model has the ability to calculate machined results very precisely.
It has already been shown that the forward simulation of manufacturing a guide vane could be validated in good agreement with the experimental data. The developed, iterative virtual method takes advantage of this outcome by correcting the cathode on the basis of the forward simulation. Each simulation provides an anode geometry which is matched with the target geometry. The difference between those two geometries, in turn, the correction of the cathode geometry can be derived. If the simulated ablation is locally greater than dictated by the target geometry, at this point material of the cathode has to be removed (Ds in Fig. 8). Where the simulated anode (blade) geometry protrudes compared to the target geometry, the gap between the cathode and blade in the final state must be reduced. In order to implement this general principle, a specific correction rule has been developed and was implemented software based. In Fig. 8, the procedure is illustrated by the example of the pressure side of the compressor vane trailing edge. In contrast to industrial practice, in which the cathode
Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071
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CIRP-1338; No. of Pages 4 F. Klocke et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
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Electrolyte low
Target geometry Blade determined by forward simulation
Cathode used in forward simulation
Δs Corrected cathode
Fig. 8. Method for correcting the cathode of the pressure side blade trailing edge.
correction is mostly made based on heuristic methods, thus an analytical possibility was created, which allows an adjustment of the cathode geometry independently of the user, cf. [22]. The target geometry and simulation results are given respectively as a point cloud with about 500 points. In each point, the correction of the projection of the distance between the target and actual geometry along the normal vector to the cathode takes place. A spline, which is defined by the determined points in the process, forms the corrected cathode geometry. In Fig. 9 the result of the forward simulation of the first iteration step is shown. On the flow surfaces the smallest deviations are achieved and at the edges, it is the only method that meets the manufacturing tolerances. Especially at the trailing edge a significant improvement is achieved compared to the traditional designed cathode with a maximum deviation of 41 mm. The result shows that at least for the analyzed blade geometry, the developed correction rule is superior to the experience-based adaptation, cf. [22].
Fig. 9. Validation of the iterative virtual cathode design.
5. Summary and conclusions With an interdisciplinary modelling approach taking gas and temperature evolution along the electrolyte flow path into account a high quality simulation of macro ECM processes for aero engine blade manufacture has been realized. Maximum deviations of less than 25 mm even in the inlet and outlet area are within requested tolerances allowing a good predictability of machining results. By an inverse simulation suitable cathode geometries can directly be calculated in a virtual design step reducing the needed efforts of experimental iteration steps.
Acknowledgements This work has been partially funded by the German Federal Land NRW within the project EFRE/Ziel 2-Forschungsvorhaben EF 2037 ‘‘Vorschmieden und elektrochemische Fertigbearbeitung von Nickelbasis-Turbinenschaufeln fu¨r 700 8C Dampfkraftwerke’’. The authors also thank the German Research Association DFG for their support within the Transregional Collaborative Research Center SFB/TRR 136 ‘‘Funktionsorientierte Fertigung auf Basis charakteristischer Prozesssignaturen’’, Subproject F03.
References [1] Klocke F, Klink A, Veselovac D, Aspinwall DK, Soo SL, Schmidt M, Schilp J, Levy G, Kruth JP (2014) Turbomachinery Component Manufacture by Application of Electrochemical, Electrophysical and Photonic Processes. CIRP Annals – Manufacturing Technology 63(2):703–726. [2] Klocke F, Zeis M, Harst S, Klink A, Veselovac D, Baumga¨rtner M (2013) Modeling and Simulation of the Electrochemical Machining (ECM) Material Removal Process for the Manufacture of Aero Engine Components. Procedia CIRP 8:265–270. [3] Klocke F, Zeis M, Klink A, Veselovac D (2013) Technological and Economical Comparison of Roughing Strategies via Milling, Sinking-EDM, Wire-EDM and ECM for Titanium- and Nickel-based Blisks. CIRP Journal of Manufacturing Science and Technology 6(3):198–203. [4] Klocke F, Zeis M, Klink A, Veselovac D (2013) Experimental Research on the Electrochemical Machining of Modern Titanium- and Nickel-based Alloys for Aero Engine Components. Procedia CIRP 6:369–373. [5] Kubeth H (1965) Der Abbildungsvorgang zwischen Werkzeugelektrode und Werkstu¨ck beim Elektrochemischen Senken, (Dissertation) RWTH Aachen University. [6] Pahl D (1969) U¨ber die Abbildungsgenauigkeit beim elektrochemischen Senken, (Dissertation) RWTH Aachen University. [7] De Silva AKM, Altena HSJ, McGeough JA (2003) Influence of Electrolyte Concentration on Copying Accuracy of Precision-ECM. CIRP Annals 52(1):165–168. [8] Deconinck D, Van Damme S, Deconinck J (2012) A Temperature Dependent Multi-ion Model for Time Accurate Numerical Simulation of the Electrochemical Machining Process. Part II: Numerical Simulation. Electrochimica Acta 69:120–127. [9] Van Tijum R, Pajak PT (2008) Simulation of Production Process using the Multiphysics Approach: The ECM Process. COMSOL Conference. [10] Shimasaki T, Kitamura T, Kunieda M (2014) Fundamental Study of ECM Gap Phenomena Using Transparent Electrode. Proceedings of the International Symposium on Electrochemical Machining Technology INSECT, 135–143. [11] Rebschla¨ger A, Kollmannsperger R, Ba¨hre D (2014) Video Based Process Observations of the Pulse Electrochemical Machining Process at High Current Densities and Small Gaps. Procedia CIRP 14:418–423. [12] Klocke F, Zeis M, Herrig T, Harst S, Klink A (2014) Optical In Situ Measurements and Interdisciplinary Modeling of the Electrochemical Sinking Process of Inconel 718. Procedia CIRP 24:114–119. [13] Koyano T, Kunieda M (2013) Micro Electrochemical Machining using Electrostatic Induction Feeding Method. CIRP Annals – Manufacturing Technology 62(1):175–178. [14] Hackert M (2009) Entwicklung und Simulation eines Verfahrens zum elektrochemischen Abtragen von Mikrogeometrien mit geschlossenem elektroly-tischen Freistrahl, (Dissertation) TU Chemnitz. [15] Kozak J, Rajurkar KP, Balkrishna R (1996) Study of Electrochemical Jet Machining Process. Journal of Manufacturing Science and Engineering – Transactions of ASME 118(4):490–498. [16] Stephen A, Vollertsen F (2010) Mechanisms and Processing Limits in Laser Thermochemical Machining. CIRP Annals – Manufacturing Technology 59(1):251–254. [17] De Silva AKM, Pajak PT, McGeough JA, Harrison DK (2011) Thermal Effects in Laser Assisted Jet Electrochemical Machining. CIRP Annals – Manufacturing Technology 60(1):243–246. [18] Hinduja S, Kunieda M (2013) Modelling of ECM and EDM Processes. CIRP Annals – Manufacturing Technology 62(2):775–797. [19] Lauwers B, Klocke F, Klink A, Tekkaya AE, Neugebauer R, Mcintosh D (2014) Hybrid Processes in Manufacturing. CIRP Annals – Manufacturing Technology 63(2):561–583. [20] Klocke F, Zeis M, Herrig T, Harst S, Klink A (2014) Experimental and Numerical Analysis of Gas Evolution and Transport during Electrochemical Machining and their Effect on Material Removal. Proceedings of INSECT, 219–226. [21] Klocke F, Zeis M, Harst S, Herrig T, Klink A (2013) Analysis of the Simulation Accuracy of Electrochemical Machining Process Based on the Integration Level of Different Physical Effects. Proceedings of INSECT, Vol. 7, 165–170. [22] Zeis M (2015) Modellierung des Abtragprozesses der elektrochemischen Senkbearbeitung von Triebwerksschaufeln, (Dissertation) RWTH Aachen University.
Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071
CIRP-1338; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Interdisciplinary modelling of the electrochemical machining process for engine blades F. Klocke (1), M. Zeis *, A. Klink Laboratory for Machine Tools and Production Engineering WZL, RWTH Aachen University, Steinbachstr. 19, 52074 Aachen, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Electrochemical machining (ECM) Modelling Engine blade
In this paper an interdisciplinary simulation model of the electrochemical machining (ECM) process for aero engine blades is set up. Simulation results of a compressor vane are presented and compared to optical measurements of actual manufactured workpieces. The simulation model is based on conservation equations for the electric field, fluid flow and heat transfer in combination with analytical functions for the influence of temperature and gas evolution on the specific electrical conductivity. Validation is done by optical in situ measurements. Finally construction rules for an inverse modelling approach are examined and simulation results of the calculated cathode geometry are presented. ß 2015 CIRP.
1. Introduction The major advantages of electrochemical machining (ECM) are its process specific characteristics of high material removal rate in combination with almost no tool wear and no thermally or mechanically damaged workpiece rim zones. Because of cost intensive tool pre-developing processes and rather high investment outlays for the machine tools, however, ECM is specifically used in large batch size production [1]. Due to these aspects ECM represents an important alternative manufacturing technology for turbomachinery components. The current development to increase propulsive efficiency by higherpressure ratio as well as through higher temperature combustion (need for high temperature resistant materials) requires an efficient machining of new designs and advanced materials. Conventional milling nowadays reaches its technological and economical limits especially for the adequate processing of selected difficult-to-cut Nibased alloys [2,3]. Thus, ECM gains more and more importance for the machining of appropriate aero engine blade geometries in serial production. ECM additionally allows the direct production of finishing surface qualities even during rough machining operations, which eliminates the need for further treatment like cost-intensive finish milling steps or grinding and polishing operations [2]. Main reason for high tool costs during ECM is an only knowledge-based, iterative cathode designing process. After a test run the produced workpiece has to be measured and the difference between target and actual geometry due to locally changed electrolysis conditions is subtracted from the cathode and so forth. On the other hand the theoretic background of all physical aspects involved during ECM is very well known, but up to now no comprehensive and interdisciplinary modelling approach is available for the precise simulation of the ECM process for
* Corresponding author. Tel.: +49 241 8027467; fax: +49 241 8022293. E-mail address: [email protected] (M. Zeis).
turbomachinery components and especially blade geometries [2]. First models describing the material removal along the electrolyte flow path in general were developed based on experimental results of standardized tests for different materials, see [4]. Kubeth for example described the basics on the reproduction of the tool electrode geometry and Pahl focused on the achievable geometrical precision [5,6]. Further research e.g. by De Silva et al. focused on the influence of electrolyte concentration on process performance [7], or the modelling of temperature aspects by Deconinck [8]. A first so-called ‘‘Multiphysics Approach’’ for the simulation of ECM processes was presented by Van Tijum et al. [9]. Current research focuses on the study of gap phenomena using transparent electrodes [10] and highspeed camera systems [11,12]. Also process analysis and modelling activities for ECM micro machining [13], electrolyte jet machining [14,15] and Laser-assisted (Jet-) ECM [16,17] are taking place. A recent advanced overview on all ECM simulation approaches is given in [18]. Further details regarding machining of turbomachinery components and hybrid approaches are given in [1,19]. For macro ECM processes temperature and gas evolution affect the conductivity of the electrolyte along the flow path significantly and thus lead to local deviations in dissolving rates [12], Fig. 1. The
Fig. 1. Fluid-dependent material removal during ECM, [12].
http://dx.doi.org/10.1016/j.cirp.2015.04.071 0007-8506/ß 2015 CIRP.
Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071
G Model
CIRP-1338; No. of Pages 4 2
F. Klocke et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
formation of a non-equidistant working gap has therefore especially to be taken into account for the modelling of ECM blade manufacture. In this paper an interdisciplinary simulation model of the ECM process for aero engine blades is set up. Simulation results of a compressor vane are presented and compared to optical measurements of actual manufactured workpieces. The simulation model is based on conservation equations for the electric field, fluid flow and heat transfer in combination with analytical functions for the influence of temperature and gas evolution on the specific electrical conductivity. Validation is done by optical in situ measurements. Finally, construction rules for an inverse modelling approach are examined and simulation results of the calculated cathode geometry are presented.
the experimental results. Furthermore the amount of gas at the end of the electrolyte gap was measured and showed good accordance to the calculated volume, cf. [12]. A comparison of simulated heat-transfer based on Joule heating and according thermography camera recordings is shown in Fig. 3. As the emissivity is unknown, no quantitative values can be given. The qualitative images show a good accordance. The temperature development along the electrolyte channel shows constantly increasing values (horizontal profile) and relatively lower values in areas with high flow (vertical profiles). Caused by anode and cathode materials different heat conductions – shown both in simulation and experiment – are taking place, cf. [12].
2. Interdisciplinary modelling approach Basis of the interdisciplinary model – which is described in detail in [12] – is the description of the anodic metal dissolution by Faraday’s law. The first extension is the electric field, which is modelled by the Maxwell equations. As the electrical properties of the electrolyte are changing along the working gap, it is necessary to model these changes with the Navier–Stokes equations and the energy conservation equation. With this set of conservation equations it is possible to compute a laminar flow effectively. But because the fluid flow can become turbulent in the working gap, a turbulence model has to be added. For the turbulent flow in an electrolyte channel under typical macro ECM process conditions for blade applications the k–e-model describes the behaviour the best. In most former models the electrochemical gas evolution at the electrodes was not considered. But due to the high volume fraction of gas in electrolyte during ECM it is necessary to model the evolution and transport of that gas as well as its influence on the electrical conductivity. For numerical reasons only hydrogen as the major gas during ECM is modelled [12]. Gas evolution itself – as an essential step for building up a simulation model of the macroscopic ECM-process – can be described by the Butler–Volmer equation as a function of the local state variables pressure and temperature. Once evolved at the cathode the hydrogen and the electrolyte form a two-phase flow which is most effectively simulated as bubbly-flow. The influence of the non-conductive hydrogen on the electrical conductivity k of the electrolyte is approximated best by using the Bruggemann equation, cf. [20]. As the fluid simulation is now strongly coupled to the electric field and the temperature, these aspects have to be computed simultaneously in a first step. The material removal is calculated afterwards – due to the need for numerical stability and efficiency – in a second step with the state variables as an input from the first step, cf. [20]. The new modelling approach for gas and temperature evolution was validated by an alignment between simulation results and according optical in situ measurements. Fig. 2 shows that the boundary layer of the bubbly-flow in the simulation grows in the same way compared to the region with high gas content from
Fig. 3. Comparison of thermography camera recordings (a) and heat-transfer simulation (b), based on [12].
Fig. 4 shows a comparison of simulation results for the ECM machining of reference geometry to verify the performance of the new interdisciplinary model. It can be seen that the simulation is in a very good accordance to the experimental results [12] and much better than the industrially established cos(w)-simulation [18]. In contrast to former simulations also the downstream area in the side gap of the outlet shows no deviation, cf. [1,21].
z Inlow
x
Feed rate
Outlow
Exp. Cos(φ)
2 mm
Sim.
Fig. 4. Comparison of simulation results (standard cosine and interdisciplinary approach with consideration of gas and temperature evolution) and experiment for machining simplified macro geometry.
3. Simulation of the removal process of engine blades
Fig. 2. Validation of gas evolution simulation (a) via high-speed camera recordings (b), based on [12].
As a specific application example the simulation model is applied to the guide vane of a multistage axial compressor. The actual production of the analyzed compressor vane was made by the industrial partner Leistritz GmbH (LTT). For this purpose, first the volume of the shear blank from Inconel 718 is redistributed over a full-forward cross-flow process into a preform. In the following rough-forging process the initial geometric contour for the electrochemical sinking is then created. For the sake of clarity in Fig. 5 the intermediate steps waterjet cutting of the excess material and pre-milling of the blade root and head have been omitted. After the ECM process, where the blade surfaces with leading and trailing edge and the annulus collectors are manufactured in one operation, finally blade root and head would
Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071
G Model
CIRP-1338; No. of Pages 4 F. Klocke et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
3
Fig. 5. Demonstration blade and manufacturing process chain. Fig. 7. Phenomena at the trailing edge towards the end of sinking.
be finished by profile grinding completing the whole process chain. The compressor guide vane has tolerances of 50 mm on the blade surfaces and 80 mm on leading and trailing edge. In anticipation of the presented simulation results it should be noted at this point that the simulation relates to the third cycle of geometric cathode tool design done by the industrial partner LTT based on the cos(w)-method (cf. Fig. 4). The flushing direction of the electrolyte was realized in the opposite direction of the aerodynamic flow direction from trailing to leading edge which generated better machining results. Nevertheless, generally still significant deviations between the machined blade contour and the nominal data occurred, Fig. 6. While the blade surfaces are already mapped precisely, at both edges still strong differences from the target geometry given from design can be seen, cf. [22]. Maximum deviations at the leading edge are 83 mm (left detail) and in the flattened area at the suction side of the trailing edge about 81 mm (right detail). For the sake of clarity these values are not shown in Fig. 6 as well as due to the fact that the differences between simulation results and measured machined surface are in the focus.
However, in addition to the purely geometrical comparison, the simulation also opens the possibility to better understand certain results of the mapping process to thereby adjust the process based on knowledge. As one representative example, the influence of different physical effects on the blade trailing edge and thus the inlet side of the electrolyte are discussed, Fig. 7. Due to the sharp edges of the cathode geometry on the downstream side above and below the main flow a dead water region develops. On the one hand here locally process heat accumulates and provides an increased electrical conductivity. On the other hand this effect leads in this area to an increased accumulation of hydrogen gas, which results in a reduction of conductivity. The main flow is deflected upon the trailing edge and accelerated, so that the static pressure decreases. According to the ideal gas law this effect leads locally to an expansion of the hydrogen gas, whereby the gas volume fraction also increases. Further, in Fig. 7 it can be seen that the suction side flow is accelerated slightly faster than on the pressure side, resulting as described in the field of higher gas volume fraction. Due to the geometric conditions, however, the pressure side recirculation region develops slightly larger, so that the influence of temperature predominates in this region. These effects lead to the fact that gas and temperature influence – related to the conductance – are roughly balanced on inlet suction side, while on the pressure side due to temperature a higher conductivity prevails. In total, these conditions result in the fact that the blade trailing edge receives a flattening on the pressure side, while the replication accuracy on the suction side is within the tolerances, cf. [22]. 4. Cathode design for the manufacture of engine blades
Fig. 6. Comparison of simulation and machined geometry with some representative absolute values of the difference between both geometries.
In the global view of Fig. 6 a good accordance between the simulation results and the actual manufactured blade can be seen. The absolute value of maximum deviation on the blade surfaces is about 15 mm, and is well within the specified tolerance band of 50 mm. In the area of the blade leading edge (left detail), the calculated geometry shows a very similar curvature to the machined blade. But in this area the largest deviation of 21 mm occurred, which corresponds simultaneously to the overall highest difference. The blade trailing edge could be calculated very precisely with a maximum deviation of only 11 mm. Summarized it can be stated that the interdisciplinary simulation model has the ability to calculate machined results very precisely.
It has already been shown that the forward simulation of manufacturing a guide vane could be validated in good agreement with the experimental data. The developed, iterative virtual method takes advantage of this outcome by correcting the cathode on the basis of the forward simulation. Each simulation provides an anode geometry which is matched with the target geometry. The difference between those two geometries, in turn, the correction of the cathode geometry can be derived. If the simulated ablation is locally greater than dictated by the target geometry, at this point material of the cathode has to be removed (Ds in Fig. 8). Where the simulated anode (blade) geometry protrudes compared to the target geometry, the gap between the cathode and blade in the final state must be reduced. In order to implement this general principle, a specific correction rule has been developed and was implemented software based. In Fig. 8, the procedure is illustrated by the example of the pressure side of the compressor vane trailing edge. In contrast to industrial practice, in which the cathode
Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071
G Model
CIRP-1338; No. of Pages 4 F. Klocke et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
4
Electrolyte low
Target geometry Blade determined by forward simulation
Cathode used in forward simulation
Δs Corrected cathode
Fig. 8. Method for correcting the cathode of the pressure side blade trailing edge.
correction is mostly made based on heuristic methods, thus an analytical possibility was created, which allows an adjustment of the cathode geometry independently of the user, cf. [22]. The target geometry and simulation results are given respectively as a point cloud with about 500 points. In each point, the correction of the projection of the distance between the target and actual geometry along the normal vector to the cathode takes place. A spline, which is defined by the determined points in the process, forms the corrected cathode geometry. In Fig. 9 the result of the forward simulation of the first iteration step is shown. On the flow surfaces the smallest deviations are achieved and at the edges, it is the only method that meets the manufacturing tolerances. Especially at the trailing edge a significant improvement is achieved compared to the traditional designed cathode with a maximum deviation of 41 mm. The result shows that at least for the analyzed blade geometry, the developed correction rule is superior to the experience-based adaptation, cf. [22].
Fig. 9. Validation of the iterative virtual cathode design.
5. Summary and conclusions With an interdisciplinary modelling approach taking gas and temperature evolution along the electrolyte flow path into account a high quality simulation of macro ECM processes for aero engine blade manufacture has been realized. Maximum deviations of less than 25 mm even in the inlet and outlet area are within requested tolerances allowing a good predictability of machining results. By an inverse simulation suitable cathode geometries can directly be calculated in a virtual design step reducing the needed efforts of experimental iteration steps.
Acknowledgements This work has been partially funded by the German Federal Land NRW within the project EFRE/Ziel 2-Forschungsvorhaben EF 2037 ‘‘Vorschmieden und elektrochemische Fertigbearbeitung von Nickelbasis-Turbinenschaufeln fu¨r 700 8C Dampfkraftwerke’’. The authors also thank the German Research Association DFG for their support within the Transregional Collaborative Research Center SFB/TRR 136 ‘‘Funktionsorientierte Fertigung auf Basis charakteristischer Prozesssignaturen’’, Subproject F03.
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Please cite this article in press as: Klocke F, et al. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.071