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Die-elasticity for precision forging of aerofoil sections using finite element simulation
Journal of Materials Processing Technology 76 (1998) 56 – 61
Die-elasticity for precision forging of aerofoil sections using finite element simulation H. Ou *, R. Balendra Design, Manufacture and Engineering Management, Uni6ersity of Strathclyde, Glasgow, G1 1XJ, UK Received 25 May 1997; received in revised form 12 June 1997
Abstract Precision forging of material into turbine blades needs a clear understanding of the prevailing parameters in forging, appropriateness of preform design, process simulation and techniques for compensating component form errors due to die-elasticity. With this in mind, simulations are conducted to analyses the material flow during forging of aerofoil sections, forging force history, contact pressure distribution between die and component, and the elastic deflections of the forging dies are investigated using finite element simulation. Further, the compensation of die-elasticity is proposed by modifying die profiles in response to die deflections based on the nominal dimensions of forging dies. The minimisation of form errors of aerofoil sections due to die-elasticity is derived by iterations using FE. The results obtained enable the quantitative estimation of die-elasticity in precision forging of aerofoil sections, and the technique for compensating component-form errors to achieve net-shape forming production. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Precision forging; Aerofoil section; Die-elasticity; FE simulation
1. Introduction Precision forging of aerofoil sections of a turbine blade is characterised by non-uniform material flow requirements, continuously changing thermal balance at high temperature, location of the preform prior to forging, elastic behaviour of forging dies and press. As the accuracy of aerofoil sections depends on many factors including die-elasticity in forging, thermal deflections and deformation of component upon cooling, one of the main objectives of attempting to forge the net-shape of aerofoil sections is to eliminate the need for subsequent material-removal of small amount of aerospace materials. However, die deflections during forming operations is a major factor influencing form errors in forged aerofoil components. The compensation of such form errors requires not only a CAD/ CAM system for dealing with aspects of geometry of aerofoil sections and configuration of forging dies, calculation of material flow and forging force requirements, but also methods of proper preform design, * Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S 0 9 2 4 - 0 1 3 6 ( 9 7 ) 0 0 3 1 5 - 4
techniques for heat treatment and lubrication, and compensation of component form errors. Research in forging of aerofoil sections has focused on material flow and prescription of preform design with different methods. Slip-line field technique was used to determine the working pressure at cross-sections and compared with experimental results derived by pressing pure lead specimen [1]. A CAD/CAM system for forging of turbine blades was developed using the slab method to predict loads, the optimum die design and preform position, and the minimum stock volume necessary to fill the die cavity [2]. Physical modelling was used to derive the material flow and pressure contours on the dies for 2D aerofoil sections with relatively cheap tools and simple machinery [3]. Research has also been conducted using FE simulations to evaluate preform specifications, forming loads and frictional effects, and the influence of press elasticity on the accuracy of components [4–6]. The elastic deflection of dies and the thermal contraction of aerofoil section were calculated at the forging temperature up to 600°C [7]. Other studies referred to process development, the mechanical properties of the forged compo-
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
nents and the limitation to forge aerofoil sections [8,9]. The application of an expert system to the solution of problems associated with forging sequence design for turbine blades was also proposed [10]. Due to nonuniform material flow, non-linear interaction friction between dies and aerofoil sections, it is difficult to predict die characteristics and, in particular, to compensate for component form errors. Therefore, further research on this subject needs to be addressed for a cost-effective approach for forging of aerofoil components within the required accuracy specification. The reported research contains a detailed analysis of factors which influence the precision forging of aerofoil sections and examines the compensation for die elastic deflections. Using ABAQUS [11], the non-uniform material flow in forging process, forging force history, contact pressure distribution at the interface between die surface and aerofoil section were studied by considering different friction conditions. In order to compensate component-form errors resulting from dieelasticity, the die elastic deflections were derived by defining the elastic and plastic properties of the component and the forging dies. The compensation of die-elasticity was introduced by modifying the nominal die profiles in the way that would counteract the die elastic-deflections. The results suggest that the form errors of aerofoil sections could be minimised and eliminated at the design stage by using finite element simulation techniques.
57
ABAQUS was used for the process simulation because of its capability of dealing with non steady-state deformation process and large sliding contact problems with definition of different friction conditions. Planestrain elements CPE4R were used to define both the component and the forging dies, while the interface behaviour between the component and the dies was modelled by the contact pairs by the description of Coulomb friction. The tool steel for forging dies was assumed to be elastic with a Young’s modulus of E= 210 GPa and Poisson’s ratio n= 0.3; the material property of the aerofoil component was defined as s = 120(1.0+o P)0.25 with a Young’s modulus of E=80 GPa and Poisson’s ratio n= 0.3, respectively. The effect of strain rate and temperature distribution in the forming process was neglected in this research. To investigate forging process at different friction conditions, the coefficient of Coulomb friction was assumed to be 0.03, 0.1 and 0.2.
2. Process modelling The precision forging of aerofoil sections from the high temperature alloys requires several stages of forming which includes extrusion, upsetting, preforming, and final forging with other operations such as heat treatment and lubrication. However, the ultimate dimension and profile of aerofoil components depends on the last forging operation which is influenced by several factors. Finite element simulation would enable detailed analysis of the forging process with different preforms and forging conditions. Further, the dimensional accuracy of forged aerofoil components can be derived with the definition of deformation characteristics of component and die, and interfacial contact properties. As shown in Fig. 1(a), the geometric description of the forging dies and aerofoil sections considered in this research was transposed from design specifications. The following geometric modelling, FE mesh generation and post processing for process simulation were implemented using PATRAN [12]. Fig. 1(b) shows the initial mesh of the forging dies and preform. FE code
Fig. 1. (a) Solid model of dies and aerofoil sections; (b) FE mesh of dies and aerofoil component.
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
58
Fig. 2. Aerofoil deformation in forming process.
displacement of the upper die, the pressure distribution shifts in an asymmetric pattern, which is attributed to the effect of the varying die profile, and the slope of die-parting line. Such non-uniform contact pressure also indicates that non-uniform elastic deflection along die surfaces and consequently, form errors in aerofoil section would occur during the forging process. Friction between the die and component has an influence on material flow, forming force history and pressure contours on the forging dies. The effect of different friction conditions was investigated by defining friction using values m =0.03, 0.1 and 0.2; the corresponding changes of contact pressure distribution are shown in Fig. 4(b). The results suggest that there is only a slight change in plastic deformation and material flow when friction conditions are different, while substantial changes in pressure contours are observed due to friction. Further, the variation of contact pressure at different friction conditions would result in corresponding changes in the required forging force. Fig. 5 shows the forging force history with different friction coefficients. Accordingly friction is a major factor of die elastic deflection.
3. Results and discussion
3.2. Die-elasticity 3.1. Material flow and die-ca6ity filling The material flow and die-cavity filling would enable the derivation of the information for preform design and sequence planning, while the forging force history is a major consideration for determining the capacity of the forming press. Another relevant parameter is the contact pressure distribution at the interface of the die and component, which introduces die elastic deflections and is an indicator of tool wear and life. With the consideration of the above factors, the process simulation for forging aerofoil sections was conducted with the developed FE model. The material flow and mesh distortion of the aerofoil section indicate a well distributed plastic deformation and sufficient die-cavity filling during the forming process, as is shown in Fig. 2(a) –(d). For the given angular orientation of the dieparting line and the differences at the two landing edges, the maximum plastic strain occurs at the left side with a maximum value of 1.56. Fig. 3(a) shows the contours of equivalent plastic strain at the final stage of forming cycle, which suggests that severer plastic deformation of occurs at the landing area. Fig. 3(b) shows the normal stress distribution on the forging dies and aerofoil section. The contact pressure distributions during the forging process at the material/die interface are shown in Fig. 4(a). The peak pressure is 933 MPa near the centre of the die. At the initial stage of forging, the pressure distribution is similar to upsetting, and has a more symmetrical distribution about the centre. With further
The final dimensions of aerofoil sections are achieved by the configuration of forging dies during forming process. Due to die elastic deflection, the aerofoil sections forged would consist of form errors which correspond to die deflections. Die deflections in both, horizontal and vertical directions, with friction coefficient of m = 0.1 are sown in Fig. 6(a). The die deflection distributions in the horizontal and vertical directions for both, upper and lower dies show maximum deflections of 67 and 57.5 mm in vertical direction, respectively; the larger deflections near the centre position of forging dies suggest that the aerofoil form errors are greater where the aerofoil section is thickest. Both upper and lower dies sustain an average horizontal deflection in the range from 20 to 30 mm in opposite directions; this results from the horizontal forces on upper and lower dies due to the slope of die-parting line. On the other hand, the difference of die deflections at the landing edges reflects the effect of local shear stress and geometry; this results in larger deflections of the upper die at the right side and of the lower die at the left side. In such circumstances, additional processing has to be introduced to remove small amounts of material. Die deflections under different friction conditions are also illustrated in Fig. 6(b), (c). The change of friction coefficients resulted in a substantial variation of die deflections. The increase of friction coefficient from 0.1 to 0.2 leads to the peak deflections of 80.1 and 68.1 mm for upper and lower dies in the vertical direction, and
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
59
Fig. 3. (a) Contour plot of equivalent plastic strain; (b) contour plot of normal stress.
the horizontal deflections of 35.1 and 29.9 mm, respectively. On the contrary, an obvious reduction of die deflections is observed when friction coefficient is defined as m= 0.03. This indicates that lubrication should be taken into account while estimating die-elasticity.
3.3. Compensation of die deflections In forging process, the thickness of aerofoil components along the cross-section is controlled by different methods for different forming presses. However, the form errors derived from die deflections would have to be compensated. The trial and error approach of modifying the nominal die contour in forging operation is
commonly used in industrial production. To improve the production efficiency, the die design iterations could be reduced by predicting the elastic deflection of forging dies at the design stage. In this research, the die elastic deflections with nominal die profiles, representing a function of forging parameters, need to be compensated with more aerofoil material in the mid-section. Therefore, the compensation of die-elasticity was implemented by modifying the nominal die profile with the amount of die deflections in opposite directions for both upper and lower dies. Following such modification, the aerofoil form errors due to die deflections were expected to be smaller than the previous one, although they are not necessarily eliminated after only one or two modifications. How-
Fig. 4. Contact pressure distribution: (a) m= 0.1; (b) effect of friction conditions.
60
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
Fig. 5. Forging forces at different friction conditions.
ever, further FE simulations of compensation would lead a further reduction of aerofoil form errors resulting from die deflections. With this approach, the elimination of component form errors due to die-elasticity could be achieved after several iterations of FE simulation.
When friction is m = 0.1, Fig. 7(a) shows the component form errors due to die deflections of upper and lower dies, after the modification of die profiles. Compared to die elastic deflections without modification in Fig. 5(a), the results suggest that a thinner middle cross-section of the aerofoil section would be produced, which means an over compensation with negative form errors from −15 to − 20 mm in vertical direction for both lower and upper dies, although the absolute value of form errors for this modification is only 28% comparing to the form errors without modification. To correct the over compensation, several other modifications of die profiles were tried by using a weighted compensation factor, Kc, between 0.5 and 0.9. It was noted that the weight factor of 0.7 would enable the minimisation of form errors due to die-elasticity. As shown in Fig. 7(b), the die elastic deflections in this compensation only result in an average of 2.5 mm form errors for the lower and upper dies in horizontal direction, the maximum form error being 5 mm in vertical direction for the upper die. The final aerofoil form
Fig. 6. Die deflections at different friction conditions: (a) m= 0.1; (b) m= 0.03; (c) m= 0.2.
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
61
Fig. 7. Form errors of forging dies after compensation: (a) first compensation; (b) further compensation.
errors due to die-elasticity are significantly reduced to the value B8 mm, compared to 125 mm total aerofoil form errors without compensation. Referring to Fig. 5(a), a substantial improvement in the accuracy of forged aerofoil sections has been derived using the proposed FE simulation.
4. Conclusions The FE simulations on die-elasticity in forging aerofoil components and compensation of component form errors from die deflections would enable the following conclusions: (1) With data on material flow and die-cavity filling in the forging of aerofoil sections, the asymmetric distribution of contact pressure between dies and component occurs; this is attributed to the die configuration, friction condition and orientation of the die-parting line. (2) Friction is a major factor which influences contact pressure distribution and forging force. The increase of friction would result in the increase of contact pressure, forging force and larger die deflections. (3) In the forming process, die deflections with the nominal die profiles lead to component form errors which are greater in the middle of the cross-section. The vertical die deflections refer to the normal contact pressure distributions, while the horizontal die deflections result from the horizontal force, local shear stress and geometry of the land. (4) Aerofoil form errors due to die-elasticity could be compensated by modifying the die configuration based on die deflection values. The minimisation of component form errors due to die-elasticity could be derived
.
by using a weighting factor Kc to determine the exact amount of modification of die profiles.
References [1] A.B. Aksenov, N.R. Chitkara, W. Johnson, Pressure and deformation in the plane strain pressing of circular section bar to form turbine blades, Int. J. Mech. Sci. 17 (1975) 681 –691. [2] T. Altan, N. Akgerman, Application of CAD/CAM in forging turbine and compressor blades, J. Eng. Power 98 (1976) 290– 296. [3] C.R. Boer, N. Rebelo, H. Rydstad, G. Schroder, Process Modelling of Metal Forming and Thermomechanical Treatment, Springe-Verlag, Berlin, 1986. [4] B.S. Kang, N. Kim, S. Kobayashi, Computer-aided preform design in forging of an airfoil section blade, Int. J. Mach. Tools Manuf. 30 (1990) 43 – 52. [5] B. Soltani, K. Mattiasson, Samuelsson; implicit and dynamic explicit solutions of blade forging using finite element method, J. Mat. Process. Technol. 45 (1994) 69 – 74. [6] R. Balendra, H. Ou, Influence of forming press elasticity on the accuracy of formed components, in: Advanced Technology of Plasticity, vol. 1, Proc. 5th Int. Conf. Technology of Plasticity, Columbus, OH, 1996, pp. 291-294 [7] X. Lu, R. Balendra, Thermoplastic considerations for simulation of nett-forming of turbine aerofoils, Proc. 11th Int. Conf. of Computer-Aided Production Engineering, London, 1995, pp. 67 – 72. [8] O. Voigtlander, G. Gunther, Isothermal precision forging— aero-engine compressor blades made in titanium alloys, Metallurgia 50 (1983) 322 – 326. [9] H. Puschnik, G. Zeiler, J. Fladischer, W. Eber, K.H. Keienburg, Udimet 720 turbine blades — production and properties, Metall. Ital. 82 (1990) 473 – 476. [10] D. Glynn, G. Lyons, J. Monaghan, Forging sequence design using an expert system, J. Mater. Process. Technol. 55 (1995) 95 – 102. [11] ABAQUS 5.5 User Manual, Hibbit, Karlsson and Sorensen, 1995. [12] PATRAN 6.0 User Manual, PDA Engineering, 1996.
Die-elasticity for precision forging of aerofoil sections using finite element simulation H. Ou *, R. Balendra Design, Manufacture and Engineering Management, Uni6ersity of Strathclyde, Glasgow, G1 1XJ, UK Received 25 May 1997; received in revised form 12 June 1997
Abstract Precision forging of material into turbine blades needs a clear understanding of the prevailing parameters in forging, appropriateness of preform design, process simulation and techniques for compensating component form errors due to die-elasticity. With this in mind, simulations are conducted to analyses the material flow during forging of aerofoil sections, forging force history, contact pressure distribution between die and component, and the elastic deflections of the forging dies are investigated using finite element simulation. Further, the compensation of die-elasticity is proposed by modifying die profiles in response to die deflections based on the nominal dimensions of forging dies. The minimisation of form errors of aerofoil sections due to die-elasticity is derived by iterations using FE. The results obtained enable the quantitative estimation of die-elasticity in precision forging of aerofoil sections, and the technique for compensating component-form errors to achieve net-shape forming production. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Precision forging; Aerofoil section; Die-elasticity; FE simulation
1. Introduction Precision forging of aerofoil sections of a turbine blade is characterised by non-uniform material flow requirements, continuously changing thermal balance at high temperature, location of the preform prior to forging, elastic behaviour of forging dies and press. As the accuracy of aerofoil sections depends on many factors including die-elasticity in forging, thermal deflections and deformation of component upon cooling, one of the main objectives of attempting to forge the net-shape of aerofoil sections is to eliminate the need for subsequent material-removal of small amount of aerospace materials. However, die deflections during forming operations is a major factor influencing form errors in forged aerofoil components. The compensation of such form errors requires not only a CAD/ CAM system for dealing with aspects of geometry of aerofoil sections and configuration of forging dies, calculation of material flow and forging force requirements, but also methods of proper preform design, * Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S 0 9 2 4 - 0 1 3 6 ( 9 7 ) 0 0 3 1 5 - 4
techniques for heat treatment and lubrication, and compensation of component form errors. Research in forging of aerofoil sections has focused on material flow and prescription of preform design with different methods. Slip-line field technique was used to determine the working pressure at cross-sections and compared with experimental results derived by pressing pure lead specimen [1]. A CAD/CAM system for forging of turbine blades was developed using the slab method to predict loads, the optimum die design and preform position, and the minimum stock volume necessary to fill the die cavity [2]. Physical modelling was used to derive the material flow and pressure contours on the dies for 2D aerofoil sections with relatively cheap tools and simple machinery [3]. Research has also been conducted using FE simulations to evaluate preform specifications, forming loads and frictional effects, and the influence of press elasticity on the accuracy of components [4–6]. The elastic deflection of dies and the thermal contraction of aerofoil section were calculated at the forging temperature up to 600°C [7]. Other studies referred to process development, the mechanical properties of the forged compo-
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
nents and the limitation to forge aerofoil sections [8,9]. The application of an expert system to the solution of problems associated with forging sequence design for turbine blades was also proposed [10]. Due to nonuniform material flow, non-linear interaction friction between dies and aerofoil sections, it is difficult to predict die characteristics and, in particular, to compensate for component form errors. Therefore, further research on this subject needs to be addressed for a cost-effective approach for forging of aerofoil components within the required accuracy specification. The reported research contains a detailed analysis of factors which influence the precision forging of aerofoil sections and examines the compensation for die elastic deflections. Using ABAQUS [11], the non-uniform material flow in forging process, forging force history, contact pressure distribution at the interface between die surface and aerofoil section were studied by considering different friction conditions. In order to compensate component-form errors resulting from dieelasticity, the die elastic deflections were derived by defining the elastic and plastic properties of the component and the forging dies. The compensation of die-elasticity was introduced by modifying the nominal die profiles in the way that would counteract the die elastic-deflections. The results suggest that the form errors of aerofoil sections could be minimised and eliminated at the design stage by using finite element simulation techniques.
57
ABAQUS was used for the process simulation because of its capability of dealing with non steady-state deformation process and large sliding contact problems with definition of different friction conditions. Planestrain elements CPE4R were used to define both the component and the forging dies, while the interface behaviour between the component and the dies was modelled by the contact pairs by the description of Coulomb friction. The tool steel for forging dies was assumed to be elastic with a Young’s modulus of E= 210 GPa and Poisson’s ratio n= 0.3; the material property of the aerofoil component was defined as s = 120(1.0+o P)0.25 with a Young’s modulus of E=80 GPa and Poisson’s ratio n= 0.3, respectively. The effect of strain rate and temperature distribution in the forming process was neglected in this research. To investigate forging process at different friction conditions, the coefficient of Coulomb friction was assumed to be 0.03, 0.1 and 0.2.
2. Process modelling The precision forging of aerofoil sections from the high temperature alloys requires several stages of forming which includes extrusion, upsetting, preforming, and final forging with other operations such as heat treatment and lubrication. However, the ultimate dimension and profile of aerofoil components depends on the last forging operation which is influenced by several factors. Finite element simulation would enable detailed analysis of the forging process with different preforms and forging conditions. Further, the dimensional accuracy of forged aerofoil components can be derived with the definition of deformation characteristics of component and die, and interfacial contact properties. As shown in Fig. 1(a), the geometric description of the forging dies and aerofoil sections considered in this research was transposed from design specifications. The following geometric modelling, FE mesh generation and post processing for process simulation were implemented using PATRAN [12]. Fig. 1(b) shows the initial mesh of the forging dies and preform. FE code
Fig. 1. (a) Solid model of dies and aerofoil sections; (b) FE mesh of dies and aerofoil component.
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
58
Fig. 2. Aerofoil deformation in forming process.
displacement of the upper die, the pressure distribution shifts in an asymmetric pattern, which is attributed to the effect of the varying die profile, and the slope of die-parting line. Such non-uniform contact pressure also indicates that non-uniform elastic deflection along die surfaces and consequently, form errors in aerofoil section would occur during the forging process. Friction between the die and component has an influence on material flow, forming force history and pressure contours on the forging dies. The effect of different friction conditions was investigated by defining friction using values m =0.03, 0.1 and 0.2; the corresponding changes of contact pressure distribution are shown in Fig. 4(b). The results suggest that there is only a slight change in plastic deformation and material flow when friction conditions are different, while substantial changes in pressure contours are observed due to friction. Further, the variation of contact pressure at different friction conditions would result in corresponding changes in the required forging force. Fig. 5 shows the forging force history with different friction coefficients. Accordingly friction is a major factor of die elastic deflection.
3. Results and discussion
3.2. Die-elasticity 3.1. Material flow and die-ca6ity filling The material flow and die-cavity filling would enable the derivation of the information for preform design and sequence planning, while the forging force history is a major consideration for determining the capacity of the forming press. Another relevant parameter is the contact pressure distribution at the interface of the die and component, which introduces die elastic deflections and is an indicator of tool wear and life. With the consideration of the above factors, the process simulation for forging aerofoil sections was conducted with the developed FE model. The material flow and mesh distortion of the aerofoil section indicate a well distributed plastic deformation and sufficient die-cavity filling during the forming process, as is shown in Fig. 2(a) –(d). For the given angular orientation of the dieparting line and the differences at the two landing edges, the maximum plastic strain occurs at the left side with a maximum value of 1.56. Fig. 3(a) shows the contours of equivalent plastic strain at the final stage of forming cycle, which suggests that severer plastic deformation of occurs at the landing area. Fig. 3(b) shows the normal stress distribution on the forging dies and aerofoil section. The contact pressure distributions during the forging process at the material/die interface are shown in Fig. 4(a). The peak pressure is 933 MPa near the centre of the die. At the initial stage of forging, the pressure distribution is similar to upsetting, and has a more symmetrical distribution about the centre. With further
The final dimensions of aerofoil sections are achieved by the configuration of forging dies during forming process. Due to die elastic deflection, the aerofoil sections forged would consist of form errors which correspond to die deflections. Die deflections in both, horizontal and vertical directions, with friction coefficient of m = 0.1 are sown in Fig. 6(a). The die deflection distributions in the horizontal and vertical directions for both, upper and lower dies show maximum deflections of 67 and 57.5 mm in vertical direction, respectively; the larger deflections near the centre position of forging dies suggest that the aerofoil form errors are greater where the aerofoil section is thickest. Both upper and lower dies sustain an average horizontal deflection in the range from 20 to 30 mm in opposite directions; this results from the horizontal forces on upper and lower dies due to the slope of die-parting line. On the other hand, the difference of die deflections at the landing edges reflects the effect of local shear stress and geometry; this results in larger deflections of the upper die at the right side and of the lower die at the left side. In such circumstances, additional processing has to be introduced to remove small amounts of material. Die deflections under different friction conditions are also illustrated in Fig. 6(b), (c). The change of friction coefficients resulted in a substantial variation of die deflections. The increase of friction coefficient from 0.1 to 0.2 leads to the peak deflections of 80.1 and 68.1 mm for upper and lower dies in the vertical direction, and
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
59
Fig. 3. (a) Contour plot of equivalent plastic strain; (b) contour plot of normal stress.
the horizontal deflections of 35.1 and 29.9 mm, respectively. On the contrary, an obvious reduction of die deflections is observed when friction coefficient is defined as m= 0.03. This indicates that lubrication should be taken into account while estimating die-elasticity.
3.3. Compensation of die deflections In forging process, the thickness of aerofoil components along the cross-section is controlled by different methods for different forming presses. However, the form errors derived from die deflections would have to be compensated. The trial and error approach of modifying the nominal die contour in forging operation is
commonly used in industrial production. To improve the production efficiency, the die design iterations could be reduced by predicting the elastic deflection of forging dies at the design stage. In this research, the die elastic deflections with nominal die profiles, representing a function of forging parameters, need to be compensated with more aerofoil material in the mid-section. Therefore, the compensation of die-elasticity was implemented by modifying the nominal die profile with the amount of die deflections in opposite directions for both upper and lower dies. Following such modification, the aerofoil form errors due to die deflections were expected to be smaller than the previous one, although they are not necessarily eliminated after only one or two modifications. How-
Fig. 4. Contact pressure distribution: (a) m= 0.1; (b) effect of friction conditions.
60
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
Fig. 5. Forging forces at different friction conditions.
ever, further FE simulations of compensation would lead a further reduction of aerofoil form errors resulting from die deflections. With this approach, the elimination of component form errors due to die-elasticity could be achieved after several iterations of FE simulation.
When friction is m = 0.1, Fig. 7(a) shows the component form errors due to die deflections of upper and lower dies, after the modification of die profiles. Compared to die elastic deflections without modification in Fig. 5(a), the results suggest that a thinner middle cross-section of the aerofoil section would be produced, which means an over compensation with negative form errors from −15 to − 20 mm in vertical direction for both lower and upper dies, although the absolute value of form errors for this modification is only 28% comparing to the form errors without modification. To correct the over compensation, several other modifications of die profiles were tried by using a weighted compensation factor, Kc, between 0.5 and 0.9. It was noted that the weight factor of 0.7 would enable the minimisation of form errors due to die-elasticity. As shown in Fig. 7(b), the die elastic deflections in this compensation only result in an average of 2.5 mm form errors for the lower and upper dies in horizontal direction, the maximum form error being 5 mm in vertical direction for the upper die. The final aerofoil form
Fig. 6. Die deflections at different friction conditions: (a) m= 0.1; (b) m= 0.03; (c) m= 0.2.
H. Ou, R. Balendra / Journal of Materials Processing Technology 76 (1998) 56–61
61
Fig. 7. Form errors of forging dies after compensation: (a) first compensation; (b) further compensation.
errors due to die-elasticity are significantly reduced to the value B8 mm, compared to 125 mm total aerofoil form errors without compensation. Referring to Fig. 5(a), a substantial improvement in the accuracy of forged aerofoil sections has been derived using the proposed FE simulation.
4. Conclusions The FE simulations on die-elasticity in forging aerofoil components and compensation of component form errors from die deflections would enable the following conclusions: (1) With data on material flow and die-cavity filling in the forging of aerofoil sections, the asymmetric distribution of contact pressure between dies and component occurs; this is attributed to the die configuration, friction condition and orientation of the die-parting line. (2) Friction is a major factor which influences contact pressure distribution and forging force. The increase of friction would result in the increase of contact pressure, forging force and larger die deflections. (3) In the forming process, die deflections with the nominal die profiles lead to component form errors which are greater in the middle of the cross-section. The vertical die deflections refer to the normal contact pressure distributions, while the horizontal die deflections result from the horizontal force, local shear stress and geometry of the land. (4) Aerofoil form errors due to die-elasticity could be compensated by modifying the die configuration based on die deflection values. The minimisation of component form errors due to die-elasticity could be derived
.
by using a weighting factor Kc to determine the exact amount of modification of die profiles.
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