3d Fem Simulation Of The Multi-stage Forging Process

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 1 9 8 ( 2 0 0 8 ) 463–470

journal homepage: www.elsevier.com/locate/jmatprotec

3D FEM simulation of the multi-stage forging process of a gas turbine compressor blade Cheng Lv a , Liwen Zhang a,∗ , Zhengjun Mu a , Qingan Tai b , Quying Zheng b a b

School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, PR China Shenyang Liming Aero-Engine Group Corporation, Shenyang 110043, PR China

a r t i c l e

i n f o

a b s t r a c t

Article history:

Due to the complicated three-dimensional geometry and the non-steady state contact

Received 2 December 2005

between the workpiece and the die surface, the simulation of blade forging process

Received in revised form

performed so far has been restricted to two-dimensional plane-strain problems or sim-

12 April 2007

plified three-dimensional deformational cases throughout which some simplifications and

Accepted 25 July 2007

assumptions are employed. This study attempts to simulate an entire forging process of a gas turbine compressor blade from a cylindrical billet to a complicated product, using 3D rigid-viscoplastic FEM. Simulation successfully predicts a complete load/time diagram and

Keywords:

deformed configurations on the preforming stages and the following forging stage. Mean-

Gas turbine compressor blade

while, the distribution of different field-variables, such as strain and temperature, were

Multi-stage forging

obtained. On the basis of these results, a change of the original forging stage is recom-

3D rigid-viscoplastic FEM

mended. The validity of simulation results was verified through comparisons with industrial trials, which were conducted on the same process parameters as those in the simulation. The simulation results may be effectively applied to other types of three-dimensional turbine blade forging processes. © 2007 Elsevier B.V. All rights reserved.

1.

Introduction

The compressor blade is one of the most important mechanical components in gas turbine engine, which plays an important role in energy transformation, and it requires highgeometrical precision and mechanical properties due to its severe working conditions. Forging of compressor blade is a complex operation to describe quantitatively due to the sensitivity of the properties of the material to process conditions and the complicated shapes of the products, which have a twist shape from the root to the end of a blade. To enable the manufacture of compressor blade with suitable mechanical properties and correct shape to be undertaken in a scientific manner, it is necessary to understand material flow, strain, strain rate, forging load and temperature histories during the

∗

Corresponding author. Tel.: +86 411 84706087; fax: +86 411 84708116. E-mail address: [email protected] (L. Zhang). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.07.032

deformation process. To achieve the above goals, the finite element method can be used for its ability to account for the complex tool/workpiece interactions and boundary conditions that would occur during the manufacturing processes. Until now, in applying FEM to gain an understanding of the thermomechanical characteristics of blade forging, most of the simulation work performed has been treated as twodimensional plane-strain problems (Morita et al., 1991; Dung and Mahrenholtz, 1982; Kang et al., 1990; Soltsni et al., 1994), which inevitably suffer from a lack of practical significance. However, blade forging is a three-dimensional process because of its twist shape from the root to the end and uneven body at different positions. Therefore, a full three-dimensional simulation is required in order to study the material flow in all the regions and obtain more realistic information to improve

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the precision of die design. In an early exercise with a simple geometry, Argyris et al. (1985) analyzed the blade forging process using the three-dimensional finite element method by considering the thermal effect, but interface friction was omitted. Isothermal forging of a turbine blade was analyzed by Yang et al. (1993) using 3D rigid-viscoplastic FEM. In the simulation, the interface friction was included and remeshing was carried out using a modular remeshing scheme. However, the arc transition between the tenon and the body on the die cavity was simplified with a right angle, which is far from the actual situation in the blade forging process. Zhan et al. (Zhan et al., 1999, 2001; Yang et al., 2002; Liu et al., 2002) simulated precision forging process of a compressor blade by 3D FEM, but the preforming stages were not considered in the analysis. In the present work, a three-dimensional finite element analysis of non-isothermal forging process of a gas turbine compressor blade is carried out, using 3D rigid-viscoplastic FEM. This simulation includes all the deforming stages from the initial cylindrical billet to the final blade and considers the frictional condition and practical arc transition between the tenon and the body. The deformational characteristics of the blade forging process are revealed and an optimized forging scheme is recommended. As an experimental validation of the simulation results, forging trials of the compressor blade have been carried out under the same forging conditions as those in the simulation.

2.

Simulation details

In the present work, the DEFORM 3D software package based on an updated Lagrangian description was employed to simulate the blade forging process. To allow the focus to be placed on the thermomechanical effects on the workpiece, a rigidviscoplastic material formulation coupled with a heat transfer formulation was used for the workpiece. The governing equations that have to be satisfied during the forging process are as follows: • Equilibrium condition: ij,i = 0

(1)

1 2

(vi,j + vj,i )

(2)

• Constitutive relation:

 ε˙ ij =

3ε¯˙ 2¯

 ij

(3)

• Incompressibility condition: ε¯˙ kk = 0

(4)

• Boundary condition: ij nij = F¯ i on Sf ,

vi = v¯ i on Sv



(5)

 ı ¯ ε¯˙ dV + k

ı˘ =

 ε˙ V ı˙εV dV −

V

V

Sf

F¯ i ıvi ds = 0

(6)

where ¯ =



3/2(ij ij )

1/2

,

ε¯˙ =



2/3(˙εij ε˙ ij )

1/2

(7)

In the above equations, , ¯ ε¯˙ , ε˙ V and ij are the effective stress, effective strain rate, volumetric strain rate and deviatory stress components, respectively. V the volume of the billet, Sf the force surface, Sv the velocity surface, F¯ i the traction stress and k is the large positive constant to penalize volume change. Eq. (6) can be converted into non-linear algebraic equations by utilizing the standard FEM discretization procedure. Due to the non-linearity involved in the material properties and frictional contact conditions, the solution is obtained iteratively. This rigid-viscoplastic material model is coupled with a heat transfer model, expressed by the energy-balance equation: ˙ =0 (kT,i ),i + r˙ − (cP T)

(8)

where k denotes thermal conductivity, T the temperature, r˙ the heat generation rate,  the specific density and cP is the specific heat. The first-term (kT,i ),i and the third-term cP T˙ represent the heat transfer rate and the internal energy rate, respectively. The rate of the heat generation in the deforming billet due to plastic deformation is given below: r˙ = ˛¯ ε¯˙

(9)

where ˛ represents the fraction of mechanical energy converted to heat, usually assumed to be 0.9. The temperature distribution of the workpiece and/or dies can be obtained readily by solving the energy balance equation rewritten, by using the weighted residual method, as

 V

• Compatibility condition: ε˙ ij =

The equations given above can be solved by a variational principle expressed as

 kT,i ıT,i dV +



V

 ˛¯ ε¯˙ ıT dV =

˙ dV − cP TıT V

qn ıT ds

(10)

S

where qn is the heat flux normal to the boundary surface, including heat loss to the environment and friction heat between two contacting objects. By applying the FEM discretization procedure, Eq. (10) can also be converted into a system of algebraic equations and solved by a standard method. In practice, the solutions of mechanical and thermal problems are coupled in a staggered manner. In the blade forging process, there are four stages during deforming, namely upsetting, heading, busting, and final forging stage, illustrated in Fig. 1. Through the first three preforming operations, a cylindrical billet is formed to a preform with a head. After preforming, the workpiece is cooled in air to room temperature, the surface is descaled, blanks are then sand blasted and reheated up to the forging temperature with a soaking time to uniform the thermal distribution inside the entire material volume. Then, the forging operation is con-

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Fig. 1 – Forming stages of the blade manufacturing process: (a) initial billet; (b) upsetting preform; (c) heading preform; (d) busting preform; (e) final forging.

Fig. 2 – Flow stress curves under different temperature: (a) 950 ◦ C, (b) 1000 ◦ C, (b) 1100 ◦ C and (d) 1150 ◦ C.

ducted to forming the final product. In order to understand and analyze the actual blade forging process, all stages are simulated, including the heat transfer from furnace to dies prior to forging. The material for the billet was a new stainless steel, which was developed for the production of gas turbine compressor blade. During hot deformation of the workpiece, strain, strain rate and temperature have a great influence on the flow and behavior of the material, which can be expressed as the equation: ¯ = (¯ ¯ ε, ε¯˙ , T)

(11)

In this paper, the material flow behavior can be realized by inputting the flow stress data, gained in the thermomechanical simulation experiments. Fig. 2 shows the flow stress curves under different temperature.

The process conditions in the FE-simulation are given in Table 1. Due to high temperature and large deformation in the process, elastic deformation is negligible and all the dies are considered as rigid bodies. The friction at the workpiece–tooling interfaces was assumed to be of shear type,

Table 1 – Process conditions for FE-simulation Preforming stages Initial workpiece temperature (◦ C) Tool temperature (◦ C) Environment temperature (◦ C) Friction factor

Forging stage

1160

1160

20 20

300 20

0.7

0.3

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Fig. 3 – FEM simulation for preforming operations: (a) initial billet; (b) upsetting preform; (c) heading preform; (d) busting perform.

Table 2 – Thermal physical properties Thermal conductivity (N/(s ◦ C)) Heat capacity (N/(mm2 ◦ C)) Heat transfer coefficient between workpiece and die (N/(s mm ◦ C)) Convection coefficient to environment (N/(s mm ◦ C)) Emissivity

36.5 7.74 11 0.02 0.8

Fig. 4 – Flow net pattern at various stages: (a) initial billet; (b) upsetting preform; (c) heading preform; (d) busting perform.

expressed as fS = mk

(12)

where fS is the frictional stress, k the shear yield stress and m is the friction factor. In the preforming operations, a friction factor of 0.7 is applied to model the dry forging conditions. While, the friction factor is assumed to be 0.3 in the following forging stage because of the lubricated conditions between the forging die and workpiece. During forging, the upper die speed changes with the ram movement of mechanical press, which can significantly affect the average strain rates and therefore stiffness within the workpiece. To model this change in compression rate, a ram-dependent die speed function is entered into the program for the preforming and forging simulations. A mechanical press with an effective load capacity of 25 MN is used in the forging operation. And the press used to preform the billet is an upsetting machine with the load capacity of 5 MN. The thermal physical properties of workpiece are given in Table 2.

Fig. 5 – Temperature distribution inside the section B–B at the end of preforming operations.

3.

Results and discussion

3.1.

Analysis of preforming operations

Fig. 3 illustrates the stages of deformation during the preforming process. Due to the large deformation occurring in the vicinity of head, the FEM mesh degenerate severely dur-

Fig. 6 – Load–time curves (preforming operations).

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Fig. 7 – FEM simulation for forging operation at a height reduction of: (a) 0.0 mm; (b) 29.7 mm; (c) 37.7 mm; (d) 40.1 mm.

Fig. 8 – Equivalent strain distribution inside the section C–C and D–D at the end of forging operation: (a) C–C and (b) D–D.

ing simulation. Therefore, remesh procedure is carried out frequently to complete the simulation. One of the most important information in metal forming analysis is the metal flow pattern. However, FEM meshs are not adequate for this purpose when remeshing is involved. In order to visualize metal flow pattern through remeshing, a procedure called flow net has been developed. Fig. 4 shows the flow net pattern of section A–A at different stages during the preforming process. It is clear that high strain caused by large deformation is concentrated in the head. This concentrated distribution of high strain leads the head material to be hardened and temperature in this region is higher than others. For the stainless steel utilized in manufacturing turbine blades, the temperature has to be kept within narrow ranges due to material strict workability windows as well as close control in microstructure specifications of the final component. High temperature in workpiece may induce some brittle phases, which can weaken the mechanical strength and the ductility of the component during its service life. When the temperature in workpiece is lower, the forging load may increase abruptly due to the sensitivity of material flow strength to temperature, and internal damages of materials like as micro-crack may occur. For the stainless steel reported in this paper, the temperature after forging is required to be larger than 950 ◦ C. Fig. 5 shows the temperature distribution inside the section B–B at the end of preforming operations. As shown in the figure, the temperature in the majority region of the perform is 1140 ◦ C, which is higher than 950 ◦ C. And due to the heat generation from deformation energy and friction, there is a slight temperature rise of about 10 ◦ C in the head region compared to the initial temperature of 1160 ◦ C. Fig. 6 shows the load–time curves on each operation for the preforming process. It can be seen that the maximum load in preforming process is about 700 kN, which takes place in the upsetting operation because of high resistance of metal flow.

The computered forming load does not exceed the effective load capacity of the upsetting machine, 5 MN.

3.2.

Analysis of forging operation

The deformed shapes of the blade at different stroke of forging operation are shown in Fig. 7. It can be seen that the spread of the blade sections resulting from height reduction takes place during the process. The elongation of the blade is small and the spread of the blade sections is almost straight so that the use of transverse sections to study the deformed characteristics would be reasonable. The equivalent strain distributions inside the cross-section C–C and D–D at the end of forging operation are shown in Fig. 8. It can be seen that large deformation takes place in the blade body, especially in the flash lands. The values of equivalent strain are found to be in the range of 1.33–1.61 in most parts of blade body. Relatively low values of equivalent strain exist in the tenon, with the range of 0.578–0.756 in most part of this region. In blade forging process, the critical deformation is an important factor, which deter-

Fig. 9 – Thermal plasticity curve of blade steel.

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Fig. 10 – Temperature distribution inside the section C–C and D–D at the end of forging operation: (a) C–C and (b) D–D.

mines the degree of deformation in single step. Fig. 9 shows the thermal plasticity curve of blade steel, which was tested by thermal compression experiments. As shown in this figure, the deformation limit in every heat number is about 0.7. Thus, the equivalent strain in blade body is much higher, exceeding the material plastic forming limit, which may induce some forming defects. As mentioned above, high temperature in workpiece may induce some brittle phases, which can weaken the mechanical strength and the ductility of the product during its service life. Therefore, the temperature distribution in workpiece is most significant during forging operation. Fig. 10 shows the temperature distribution inside the cross-section C–C and D–D at the end of forging operation. It is clear that there is little decline of temperature in blade body due to the heat generation from deformation and friction. The highest values of temperature in the central zone of cross-sections are about 1170 ◦ C at the end of forging stage. Based on physical modeling experiments, we find that this temperature value is much higher and the mechanical strength and the ductility of the final forging part, which is forged under this temperature, are much lower for its application. Fig. 11 shows the load–time curve for the forging operation. Here, the forging load increases abruptly due to flash formation. Maximum load for this finish operation is lower than 20 MN, less than the effective load capacity of the mechanical press, 25 MN.

3.3.

Optimization of forging operation

The accurate analysis of above forging operation reveals that the temperature and equivalent strain values after final

Fig. 11 – Load–time curve of forging operation.

forging stage are rather higher than the respective values. Consequently, the forging process should be amended. It is clear that the large deformation could be reduced through adding a preforging blow prior to finish forging and, at the same time, reducing the finish forging temperature to decrease the possibility of brittle phase occurrence. Thus, current industrial forging process consists of two forging steps, namely preforging and finish forging. And the finish forging temperature is reduced to 1120 ◦ C. Fig. 12 shows the distribution of field-variables inside section C–C at the end of preforging operation. The values of equivalent strain are found to be in the range of 0.422–1.07 in the cross-section. And the highest temperature values in the central zone of cross-section are about 1170 ◦ C. These temperature and strain values are a little higher, but do not affect the final forging part due to the reheating and finish forging after preforging stage.

Fig. 12 – Distribution of field-variables inside section C–C at the end of preforging: (a) equivalent strain and (b) temperature.

Fig. 13 – Equivalent strain distribution inside section C–C and D–D at the end of finish forging: (a) C–C and (b) D–D.

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Fig. 14 – Temperature distribution inside section C–C and D–D at the end of finish forging: (a) C–C and (b) D–D.

Fig. 13 shows the equivalent strain distribution inside section C–C and D–D at the end of finish forging step. As shown in this figure, the equivalent strain after finish forging is reduced greatly. The values are in the range of 0.3–0.8 in the central zone of section C–C and less values exit in the section D–D, which are rather lower than the material plastic forming limit. Fig. 14 shows the temperature distribution inside section C–C and D–D at the end of finish forging. It can be seen that little temperature change has happened compared to the initial temperature of 1120 ◦ C, which could ensure the required qualities of the final products. There is a little temperature rise of about 20 ◦ C in the flash lands due to the severe deformation and friction in that region. However, temperature change in the flash was not taken into account since these portions of materials are removed by machining after forging. Fig. 15 shows the load–time curves of optimized forging process. It can be seen that the forging load is very low in preforging stage and increases abruptly due to flash formation during the finish forging stage. Thanks to high sensitivity of flow strength to temperature, temperature reduction leads to a substantial increase of finish forging load. The maximum load

Fig. 15 – Load–time curves of optimized forging process.

in finish forging stage is 23 MN, which is much higher than the maximum load during the original forging operation, but it is lower than the effective load capacity of the mechanical press all the time.

Fig. 16 – Products through the optimized process: (a) preforming billet; (b) preforging part; (c) finish forging part; (d) final product.

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Experimental verification

After convinced by numerical simulation that the optimized forging process can give a realistic possibility for the production of gas turbine compressor blade, forging tests were performed to validate the results of FE simulation. The forging process parameters are the same as those in the optimized process. The lubricant used in the experiments was the mixture of commercial grease and MoS2 . The forging tests were conducted on a mechanical press with 25 MN load capacity for preforging and finish forging operations. And the press used to preform the billet was an upsetting machine with the load capacity of 5 MN. Fig. 16 shows the geometries of a forged blade and its preform produced with the optimized process. Compared with the simulated results shown in Figs. 3 and 7, the similarity of the geometry between the forging trials and the simulation results is clearly apparent. Meanwhile, the mechanical properties such as strength and ductility satisfy the application requirements well, according to the testing experiments. Thus, industrial trials show good agreements with the FEM simulation of the blade forming process.

5.

Conclusions

Using the rigid-viscoplastic finite element method, a threedimensional finite element analysis of non-isothermal forging of a gas turbine compressor blade is carried out, including all the deforming stages from the initial cylindrical billet to the final blade. FE analysis provides detailed information on the material flow, load, strain and temperature, which can be incorporated into process design. The conclusions with the finite element analysis can be summarized as follows: (1) At the end of preforming operations, the temperature in most parts of the workpiece is 1140 ◦ C, which is higher than the temperature corresponding to unacceptable low temperature. At the same time, the loads during the preforming operations are much lower than the effective load capacity of upsetting machine. (2) At the end of original forging operation, the values of equivalent strain in most parts of blade are rather higher, in the range of 1.33–1.61. This highly accumulated strain exceeds the material plastic forming limit and may cause some forming deficiencies. Due to heat generation from deformation energy and friction, the temperature in workpiece after forging operation is much higher than the receivable value and may induce some brittle phases which can weaken the mechanical strength of the component during its service life.

(3) On the basis of the analysis results of above forging operation, an optimized forging scheme is recommended to eliminate the strain accumulation and reduce the temperature rise in the workpiece after finish forging. In the optimized forging process, the simulation results show that the equivalent strain and temperature are reduced greatly and can ensure the required quality of the final products. Industrial trials have demonstrated the validity of simulation results.

Acknowledgement The authors would like to express their appreciation for the financial support of the National High Technology Development Program of China (2004AA503010) for the present research work.

references

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