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Procedia

Procedía Engineering 207 (2017) 520-525

www.elsevier.com/locate/procedia

International Conference on the Technology of Plasticity, ICTP 2017, 17-22 September 2017,

Cambridge, United Kingdom

Optimizing Design of Two-dimensional Forging Preform by Bidirectional Evolotionary Structural Optimization Method

N. V. Ngo, Q. C. Hsu*, W. H. Li, P. J. Huang

Department of Mechanical Engineering, National Kaohsiung University of Applied Science, 415 Chien-Kung Road, Kaohsiung 80778, Taiwan.

Preform is a step between blanking and finish forming. Design and optimization of the preform for forging would affect the material flow, forming lond, dimensi on accuracy and too l wear. In this study, analysis, simulftion and optimization process are carried out by utilizing MATLAB codes as weli as uoing finite el ement analynis software (DEFORM-2D package ) and CAD software as auxiliary tools. The results of this study are as following: ustng "(Curve Fitting" method and two tideg of reference length are the better option for the boundary fitting method. Besides, the differences between using mean stress and normal pressure as an additi on coiner ion wer e conside red. In terms of strain, -the average of effective strain is 0.(343 and the standard deviation is 0.238 when using normal procure as an addition criterion . These values are smaller than those u3ing mean stress as sio addonon criterion, in which the values are 0.674 and 0.308, rerpectively. In terms of forming load, the valun oC the former is 70 .616 tons . It is greater than valu e of the other criterion that forming load is 70.207 tons. Finally, is terms of shape, tho results 7rom normal pres sure are more complex than tho se from mean stress.

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Peer-review undhr responsibility of the scientific committee oo the International Conference on the; Technology of Plasticity. Keywords: forging; preform design; topology optimization; bi-directional evolutionary structural optimization;

1. Introduction

Forging may be defined as a manufacturing process by means of deFormation in conjunction with heating, separating, and joining of a workp i eco wMi permanent work hardening [1]. F orging is ruerently known as the of fest technology in the metal forming process. Prehistoric humans have found that by heating the sponge iron anf

* Corresponding author. Til.: +886-7-3814526 Ext 5338; Fax: +886-7-3831373. E-mail address: hsuqc@kuas.i8u.tr

Abstract

1877-7058 © 2017 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the scientific committee of the International Conference on the Technology of Plasticity. 10.1016/j.proeng.2017.10.815

knocking stone, its shape can turn into useful items [2]. Since the forging part is deformed by impact or extrusion, it has the following advantages [3]: (1) Less defects; (2) Continuous material flow, better impact resistance, good fatigue resistance and other mechanical properties; (3) Stability of geometric dimension, high reliability and suitable for mass production.

In general, forging method is difficult to manufacture the products with complex shape, die is expensive and it is not suitable for a few products. Nowadays, however, forging method is improved with high precision, complexity, and diversity. The manufacturers always want to reduce cost of forging products, and improve production efficiency. In the forging process, preform stages have the significant impacts on the quality, efficiency and cost. Therefore, the preform design has become one of the important key of forging process. In the complex shape forming, in order to avoid material failure and affect the mechanical properties, forming process is divided into multiple stages. Each stage is called as a preform design step. The preform gradually changes the shape of the billet into the desired preform, so the ultimate goal of any analytical method is to assist engineers in designing the preform stages [4].

The problems of most traditional structural optimization methods are implemented by using the evolutionary structural optimization method [5]. There are two methods, one is ESO and the other is BESO. The ESO method is to optimize the shape of the structure by gradually removing inefficient material from a structure. The stress of each part in the ideal structure should be quite similar and safe level. This concept leads to a rejection criterion based on the local stress level, where the low stress is assumed to be under-utilized and gradually removes the material. The BESO method can remove inefficient materials and add useful materials at the same time [6]. Furthermore, this method may start from designs that are much smaller than the full design domain and save time for the finite element analysis (FEA).

With the BESO algorithm, the computational efficiency and flexibility of the algorithm are improved [7]. In this study, the background meshes are created with an equally spaced grid. Each grid of background mesh can be defined as an element. The area contained in this grid is the design area of the ESO or BESO algorithm. Each element can be divided into active and inactive. The shape of the preform includes the active elements. However, the mesh boundary defined by the active elements is rough and cannot be used directly for FE simulations. A smooth contour which is acceptable for FE simulation can be obtained by extracting the boundary of active meshes and using surface approximation method to smooth the surface.

2. Research methodology

2.1. BESO method for forging preform design optimization

The BESO method has often been used for continuum structures under loading of elastic deformation. With this method, materials can be added or removed from structure simultaneously by using a certain criterion. In the forging preform design optimization, the same concept may be used: unnecessary materials can be removed while some materials can be added in the certain regions of forging structure. By the way, after some optimization iterations, the preform shape can be obtained the optimum structure for forging process. However, in the forging process, internal structure of workpiece is required to be continuum without a void, so optimization process can be only performed on the boundary of the workpiece. Before simulating FE using DEFORM-2D, curve of the boundary must be smoothed due to the complex contact conditions between workpiece and dies. Therefore, in this study, curve fitting method is used to interpolate the boundary of preform. After the FE analysis, a data tracking and an operation of interpolation process are carried out in order to track the information of meshes from final step to initial step and interpolate to background meshes. Then the activation and inactivation of background meshes can be determined in accordance with the criteria [7].

2.2. Optimization objective

The objective of this study is to obtain the best preform for forging process which enables sufficient filling of die cavity and minimum material consumption. This objective can be represented by the unfilled length and the flash length. The objective function can be calculated by performance index (PI), as shown in the following equation 1.

PI (performance index) =

Where: Su is the unfilled length; Sf is the flash length and Sd is the die cavity length. Su and Sf are shown in Fig.1. 2.3. Optimization scheme

The flowchart of the optimization scheme is shown in Fig. 2. First, the design domain is defined according to the size of the billet, the dies and the expected size of the preform. After that, the background mesh for optimization is defined. FE simulation process is implemented with initial workpiece and then PI will be checked. If PI < tolerance, optimization will be finished; whereas, geometry of forging preform will be modified. To start this modified process, data tracking is performed via DEFORM-2D. After this process, the element activation and inactivation are performed for all elements in background mesh by an optimization program that is programed by MATLAB software. The new geometry of the preform is obtained by extracting all active elements on the boundary of the background mesh. This new geometry is interpolated by using curve fitting method and then importing to DEFORM-2D for FE analysis. After the simulation is finished, the shape of simulation result is saved in the format of IGS. With the simulation results, the unfilled length (Su) and flash length (Sf) are determined and the performance index (PI) is calculated and checked again. The procedure is continued or terminated.

Fig. 1. Definition of unfilled and flash length

Fig. 2. Flowchart of the optimization scheme

2.4. Background mesh data process

In tracking point process, some points can be removed from original background mesh, so it will make some areas that cannot be determined an active mesh because each grid of this background mesh is composed of four nodes. To solve this problem, the equation 2 is used. The nodes of the area around the center will be scanned from left to right and up to down. If more than two meshes are covered in the scanning range, this mesh is regarded as the active mesh. This method reduces the volume loss effectively.

d2 = (x - x')2 + (y - y')2

Where: x and y are the coordinates of the nodes; x' and y' are the coordinates of the center of the background mesh. In the study, d2< k (d*)2/2 is used in the calculation process, d* is the background mesh side, and k is 1.05 as the allowable error ratio.

3. Results and discussions

In this study, AISI 1035 material is used. Initial workpiece temperature is 980o, shear friction factor is 0.4 and

velocity of punch is 100 mm/s. Figure 3 shows the FE model of preform and initial billet. Clearly, there is not enough material filling into the die cavity. After the BESO computation iterations, material is removed and added on the boundary of workpiece surface. A new curve of preform is formed. At the final iteration, die cavity is filled and a small flash is created. Geometry of billet and desired preform of forging part is shown as in Fig. 4.

Fig. 3. Initial preform design and forging shape at the 1st iteration.

Fig. 4. Preform design and forging shape at the 8th iteration.

3.1. Formation of boundary contours offorging preform

Evolution of preform after some iterations are shown in Fig. 5. It shows that geometry of preform is changed after each iteration. At the first iteration, geometry is simple. But at the fourteenth iteration, geometry becomes to be more complex. These geometries may be created in two ways which are studio spline and fit curve.

Table 1. The number of boundary and compensation mesh at different iterations of studio spline and fit curve.

Studio spline Fit curve

Number of Number of Number of Number of Number of

iterations boundary mesh compensation mesh boundary mesh compensation mesh

0 559 0 559 0

3 567 14 557 127

6 575 21 561 101

9 589 34 565 102

12 587 45 571 103

14 591 44 571 82

In order to compare the differences between the contours obtained by the two kinds of fit curve methods and contours obtained by the algorithm, the background mesh after curve fitting is compared with the background mesh obtained by the algorithm, which will be excluded because of the contour fitting. The number of boundary and compensation mesh of each iteration is shown in Table 1. It shows that the number of compensation for the studio spline is much lower than the fit curve because the contours of the studio spline are similar to those of the algorithm. But when the number of iterations increases, it is difficult to get a similar contour, so the amount of compensation gradually increases. The volume changes after each DEFORM iteration are about 0.1% to 0.2%.

a. Preform design after 2 iteration

b. Preform design after 6 iteration

c. Preform design after 10th iteration d. Preform design after 14th iteration

Fig. 5. Evolution process of forging preform

3.2. The objective values with normal pressure as addition criterion

BESO method is used as a materials-added method based on the threshold of normal pressure, whereas ESO method is used as materials-removal criterion based on the threshold of total velocity. The number of background mesh is 20,000. The values of Su, Sf and PI of each iteration are shown in Fig. 6 (a). It shows that those values of the previous six iterations of Su, Sf, and PI do not change significantly, and the figure 6(b) also shows that the volume increases steadily.

3.3. Comparison of different addition criteria

Figure 7(a) shows the equivalent strain using mean stress as an addition criterion when the number is about 20,000. Figure 7(b) shows the distribution of equivalent strain and it is similar to the equivalent strain distribution using normal pressure as an addition criterion. The average equivalent strain is 0.643 when using normal pressure as an addition criterion and the standard deviation is 0.298. This result is slightly less than 0.671 and 0.308 obtained by using mean stress as an addition criterion.

The load-displacement diagram is shown in Fig. 7(c), simulation process finishes when the thickness of flash is 0.2 mm. It shows that when the movement of the die is finished, the load obtained by using mean stress as an addition criterion is 70.207 tons. It is slightly less than 70.616 tons obtained by using normal pressure as an addition criterion.

In conclusion, the result of the mean stress or normal pressure is nearly similar. Using normal pressure as an addition criterion is better for equivalent strain. Using mean stress as an addition criterion is better for load. However, the preform shape obtained by using normal pressure as an addition criterion is difficult to manufacture.

The shape of the preform of this study and Y. C. Tang at al. [8] are shown in Fig. 8. It shows that the preform of this study is more complex than that of Y. C. Tang at al. [8] because there is no restriction on the position when the background box is added or removed, and then it is only curve fitting to make its smooth.

0 1 2 3 4 5 6 7 S 9 10 11 12 lî 14 15 16 17 IS 13 20

1 2 3 4 5 6 7 S 9 10 11 12 13 1+ 15 16 17 18 19 20

Fig. 6. (a) Convergence analysis of number of iterations; (b) Relationship between the rate of volume change and the number of iterations.

4 (Nodal)

19.505

5.604 MM ■

1.703 ■ ■

3.901 J

Y Loadjtons-Si)

Load Prediction

5B.974 44.230 29.487 14.743 O.OQOOO

-Tod Die (4.05 70.207) :

O.OOO J.400 , _„ 0.8.00 , 1,20 , 1.80 2.00 Strain ( Effective ) (mnvrhm)

0.000 0.850 1.70 2.55 3.40 4.25 Stroke (nun)

Fig. 7. (a) The equivalent strain, (b) distribution of equivalent strain, (c) load displacement diagram, using mean stress as a criterion.

Fig. 8. (a) The optimized preform and final forged shape of Ref. [8], (b) The optimized preform and final forged shape of this study. 4. Conclusion

In this study, the BESO method is used to optimize the forging preform design. The BESO optimization program was written by using MATLAB software, smoothed curve of forging preform is achieved by the curve fitting method, and the best preform is obtained by the optimized algorithm and simulated via DEFORM software to verify its effect. The results show that the die cavities are completely filled with minimised flashes. Although the shape of the best preform is more complex than initial billet, it is simpler than final forged shape. Besides, the proposed preform design optimization method can be used to obtain bulk forming preform design optimization within small number of iterations. Finally, the results of this study are compared with other studies.

Acknowledgements

The authors would like to acknowledge Ministry of Science and Technology, Taiwan, for their financial support for current study under project grant No. MOST 105-2221-E-151-010-.

References

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[3] S. L. Semiatin, ASM handbook volume 14 Forming and Forging, ninth ed, ASM international, 1988.

[4] S. Kobayashi, S. I. Oh and T. Altan, Metal Forming and the Finite-Element Method, first ed, Oxford University Press Inc, New York, 1989.

[5] Y. M. Xie and G. P. Steven, Evolutionary Structural Optimization, Springer, New york, 1997.

[6] X. Huang and M. Xie, Evolutionary Topology Optimization of Continuum Structures: methods and applications, First edition, John Wiley &

Sons Inc., New Jersey, 2010.

[7] B. Lu, H. Ou, Z. S. Cui, "Shape optimisation of preform design for precision close-die forging," Structural and Multidisciplinary Optimization, 44(6), 2011, pp. 785-796.

[8] Y. C. Tang, X. H. Zhou and Chen, J., "Preform tool shape optimization and redesign based on neural network response surface methodology,"

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