optimization of hot forming process using data mining ...

International Journal of Automotive Technology, Vol. 16, No. 2, pp. 329−337 (2015) DOI 10.1007/s12239−015−0035−0

Copyright © 2015 KSAE/ 083−17 pISSN 1229−9138/ eISSN 1976−3832

OPTIMIZATION OF HOT FORMING PROCESS USING DATA MINING TECHNIQUES AND FINITE ELEMENT METHOD G. J. ZHENG1, 2), J. W. ZHANG1), P. HU1, 2)* and D. Y. SHI1) 1)

School of Automotive Engineering, Dalian University of Technology, Dalian 116024, China State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian 116024, China

2)

(Received 30 August 2013; Revised 7 February 2014; Accepted 7 March 2014) ABSTRACT−In the process of hot forming, many design variables have effects on the final results in different and complex ways, such as geometry feature and forming process parameters. It is difficult to understand the relationship between design variables and results, which is very important to guide the design. In this paper, Data Mining (DM) was introduced to explore the influence of the parts geometric feature and the hot forming parameters on hot forming results of an automobile B-pillar model, and the optimum parameter ranges were determined. Firstly, a series of variable parameters were chosen and 100 groups of experimental data were generated with super Latin method, then the FEM ananlysis results were calculated respectively. Secondly, analysis and evaluation of simulation results were carried out by making full use of the Decision Tree (DT) algorithm. Finally, a series of B-pillar hot forming rules were refined, such as the initial temperature of the sheet metal should be controlled between 720 oC to 800 oC. The fillet radius is recommended to be bigger than 10mm and the height gradient should be controlled under 67mm, etc. A real B-pillar model was designed to testify the rules and the result shows that the rules are correct and effective. KEY WORDS : Hot forming, B-pillar, Geometry feature, Process parameter, Data mining

mould and the relationship between hot forming results and geometry features and process parameters are hidden in the analysis results. It is hard to find out the relationship automatically and depends more on the practical experience of engineers. A.H. Van Den Boogaard (Van Den Boogaard et al., 2008) studied the optimization of blankholder force and blank shape parameters of deep drawing of the B-pillar and the response surface method was used to find out the optimum result. Bonyoung Ghoo (Ghoo et al., 2010) studied the hot forming process of Audi B-pillar and the numerical simulation based on FEM technology and optimization design using the hybrid adaptive SHERPA algorithm were applied to improve productivity. These two methods can help to obtain a single optimum result but not a relationship between the forming parameters and the forming results. Data Mining (DM), which is based on the development of database, statistics, machine learning and expert knowledge system, is an interdisciplinary which has developed quickly in recent years (Wei et al., 2013; Lin et al., 2013). The potential correlation and laws between forming parameters and results can be collected by using Data Mining method and some useful domain knowledge between data and information be extracted finally. With the extensive application of FEM which is the most popular Computer Aided Engineering (CAE) technology currently, the simulation data have been rapidly increased. Many

1. INTRODUCTION Using Ultra-High Strength Steel (UHSS) to make automotive structural crashworthiness parts is an important method to achieve automotive lightweight on the basis of car crash safety, because the UHSS has a high potential for weight reduction and crashworthiness benefits. Currently, the hot forming technology has been applied on many structural crashworthiness parts (Jiang et al., 2012), such as door anti-collision beam, bumper, B-pillar (Long et al., 2012) and other impact components (Zhang et al., 2011). In the process of hot forming, many design variables have effects on the final results in different and complex ways (Liu et al., 2012). Understanding the relationship between the variables and the results has a positive significance to guide hot forming design. Currently, the research on hot forming technology mainly focuses on forming theory and the accuracy of the numerical simulation (Kwon et al., 2011; Bardelcik et al., 2010; Ikeuchi and Yanagimoto, 2011; Turetta et al., 2006). However, the study on the influence of parts’ geometry features and forming process parameters to the results of hot forming is limited and necessary. A large number of forming numerical simulations were done before making a real hot forming *Corresponding author. e-mail: [email protected]

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G. J. ZHENG, J. W. ZHANG, P. HU and D. Y. SHI

scholars studied the FEM results using different Date Mining methods and achieved some successes. Li DY (Li et al., 2007) discussed the integration method of finite element numerical simulation results and used rough sets and principal component analysis method to analyze FEM results. Fernandez . J (Fernandez et al., 2010) described a method based on the combination of FEM and DM techniques to set up prediction models that can be used to calculate bolted connections. and ZHAO ZJ (Zhao et al., 2010) analyzed the automobile crash simulation results by using DM method and described the application method and the process of DM in FEM environment. In summary, the DM technology not only get an optimum parameter sets from a large number of simulation datas, but also obtain some useful design programs and guidelines for future design. However, DM has not been applied in the study of the hot forming FEM results. In this paper, with the help of the self-developed hot forming production equipment and forming process analysis software named KMAS , an automobile B-pillar was designed, analyzed and produced. Firstly, numerical simulation results with various forming process parameters and geometric features were collected and cleaned. Then, a variety of DM methods were used to explore the regular pattern and discover potential knowledge of hot forming. Finally, some B-pillar hot forming rules were formed and verified by a real hot formed B-pillar. TM

2. PRE-PROCESS OF DATA MINING The Data Mining refers to extract or mine useful knowledge from a large number of data and its basic premise is to collect sufficient available data. Owing this, the data mining model can be established and evaluated, and after that, the knowledge visualization technology and knowledge representation techniques are used to provide useful knowledge for researchers and experts in the field. With the rapid development of CAE calculation ability, numerical simulation has been developed in automotive R&D and gained more and more simulation results. To perform DM among the finite element simulation

Figure 1. Data mining flow of B-pillar hot forming process.

results, the first step is to create a large number of finite element simulation models in FEM pre-process, calculate the simulation process in FEM solver and extract valid results in FEM post-process, respectively. Then the second step is to collect simulation results, form the result database and discover the patterns or extract knowledge in the field. The entire DM process of the B-pillar hot forming design and analysis is shown in Figure 1. In FEM environment, about 70% work of the data mining are mainly about the data pre-process which includes FEM model building, simulation calculation, results extraction, data integration, data conversion and data discretization, etc. 2.1. Building CAD and FEM Model for B-pillar The “Rainbow” brand vehicle is an electric car which is developed by the School of Automotive Engineering, Dalian University of Technology (DUT). The B-pillar of the car was to be manufactured by hot forming technology to gain well side impact crashworthness. 22MnB5 steel has been widely used in the hot forming field currently. Figure 2 shows the shape and size of the tensile specimen which is designed to obtain material performance of the steel. Taking temperature into consideration, the onedimensional tensile tests were finished at 600 C, 650 C, 700 C, 750 C, 800 C and 850 C, respectively, so as to obtain the steel material properties. The thermal horizontal tensile testing machine involved is made by DUT independently. Engineering stress-strain and true stress-strain conversion formula is shown below: o

o

o

εt = ln ( 1 + εe ) σ t = σ e ( 1 + εe )

o

o

o

(1)

Figure 2. Shape and size of the hot forming tensile specimen.

Figure 3. Plastic strain versus true stress curves at different temperatures.

OPTIMIZATION OF HOT FORMING PROCESS USING DATA MINING TECHNIQUES

εe, εt, σe and σt represents engineering strain, true strain, engineering stress and true stress, respectively. The plastic strain versus true stress curves under different temperatures are shown in Figure 3 by intercepting the deformation of plastic portion. There are four steps in the forming process: (1) heating sheet metal up to austenizing temperature; (2) transferring heated sheet to a press in air; (3) forming at elevated temperature and (4) quenching of formed parts in the forming tool (Choi et al., 2012). Phase transformation happens rarely because the forming time is relatively short. The phase transformation happens in the step of quenching (Choi et al., 2013) and fracture could happen in the forming process. The paper focuses on the forming performance of the steel under high temperature, that is whether fracture happens or not Thus the numerical simulation using thermal-mechanical coupled analysis in the paper considered the forming process only, with no consideration of the microstructure phase transformation in the quenching step. The tools in the simulation are assumed as a rigid body and the thermal properties are: Thermal Conductivity (TC) is 50 W/mK and Heat Capacity (HC) is 350 J/kgK. As the temperature of steel will change in the forming process, the paper takes the steel’s different thermal properties under different temperatures into consideration as shown in Table 1. The numeral simulation neglects the convictive heat transfer and the heat radiation between the steel and the air and the thermal conductivity between the sheet and the tools is 1500 w/mK. The friction between the blank and tools calculates by Coulomb’s law and the coefficient of friction is set to 0.4.

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All the pre-process operations can be finished in KMAS™, such as CAD data meshing, die-face splitting, material parameters setting, tools position, sheet metal temperature initialization, boundary condition setting, contact setting and other forming parameters setting. Figure 4 shows the completed assembly schematic of a Bpillar single action drawing. 2.2. Test Program Many design variables can affect the hot forming results, such as the mould cooling rate, material properties of steel, steel thickness and part shape, etc. It is very difficult to take so many variables into account at the same time. To reduce the difficulty of the research, only the geometric features of part and small section of hot forming parameters are considered in this paper. The design variables are fillet size of part, drawing depth, blankholder force, initial temperature of steel and mould surface. The profile of the B-pillar is shown in Figure 5. In order to improve the material flow capability of the sheet metal between mould tools, the die-faces should be smooth and continuous. Therefore some fillets with sizes range from 5 mm to 30 mm were designed to connect the side wall and the flange. Take into account the crashworthiness of the B-pillar and the space requirement of the “Rainbow” car, a boss must be designed in a certain height as shown in Figure 5 andthe high-end part of the B-pillar which marked as “H1” should be set between 60 mm to 100 mm, while the low-end part which marked as “H2” should be set between 20 mm to 35 mm. In the process of hot forming, the blank which is a type

Table 1. Thermal properties of blank sheet under different temperatures. o

Temp ( C)

400

500

600

700

800

900

TC (W/m.K) 21.7

22.7

21.7

24.5

25.6

26.6

HC (J/kg.K)

573

581

586

590

596

561

Figure 5. Geometric parameters of the B-pillar. Table 2. Parameters and value range. Parameters

Value range Lower Upper

Units

R

Fillet radius

5

30

mm

H1

The high-end height

60

100

mm

H2

The low-end height

20

35

mm

F

Figure 4. Assembly schematic of hot formed B-pillar.

Parameters description

Blankholder force

10000 50000

N

BIT

Initial temperature of blank

600

850

o

C

TIT

Initial temperature of die-face

20

70

o

C

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G. J. ZHENG, J. W. ZHANG, P. HU and D. Y. SHI

o

of sheet metal was heated to above 900 C firstly. Because the austenitizing temperature of steel is slightly lower than 900 C, so the microstructure of the sheet metal transformed to austenite at this temperature. Then the blank was applied on die-face of one of the tools (die or punch, for example) for drawing and quench. Due to the thermal radiation and the heat conduction between the blank and die-faces, the temperature of the blank has decreased before the starting the drawing process. According to the drawing velocity and the requirement of the product performance after quenching, the initial temperature of the sheet metal should be controlled between 600 C to 850 C usually. Meanwhile, the initial temperature of the die-face should be set within 20 C to 70 C because of the heat transfering from the blank to the tools. In addition, the blankholder force should be controlled with 10000 N to 50000 N. As shown in Table 2, a total of 100 cases of experimental data for B-pillar hot forming are obtained by way of the Optimum Latin Hypercube, which includes six influencing factors and each one has its own value range. o

o

o

o

o

2.3. Generating FE Models According to the parameters and their value ranges shown in Table 2, an Excel spreadsheet about experimental design is obtained as shown in Figure 6. In order to improve the efficiency of CAD model generation, a parametric B-pillar CAD model is created in CATIA environment and R, H1, H2 are specified corresponding parameters in Table 2, as shown in Figure 7. Interactive automation between CATIA and Excel can be achieved by using VAB programming as shown in Figure 8. With the help of these VBA codes, the parameters of the B-pillar can be modified according to the Excel spreadsheet content and export different surfaces to

Figure 8. Source code example about B-pillar CAD model automatical generation.

specified file path with corresponding filename automatically. Using the method introduced in Section 2.1, 100 cases of B-pillar CAD model can be formed into 100 cases of correct pre-process documents, and after calculation in batch mode, 100 cases of FE results are obtained. 2.4. Analysis of Forming Results and Data Extraction In the process of hot forming, springback, wrinkling and other forming defects rarely occurred, but local ruptures occurred commnoly as shown in Figures 9 and 10. There are two main reasons for the local rupture, one is that uneven distribution of sheet metal deformation and the other one is bad material flow capability of hot metal. When the sheet metal is heated to above 900 C, it becomes softer than that in normal room temperature and the friction coefficient of sheet metal and die-face will be increased. Material Softening leads to lower tensile strength. Bigger friction coefficient leads to bigger pressure when drawing, so the local rupture occurs more frequently in hot forming than in cold stamping. The parameters setting and geometric feature are different in hot forming from cold forming according to the fact that the hot forming and cold forming have many essential differences, and the cold forming experience is discomfortable for hot forming. Based on such a situation, the local thinning and o

Figure 6. Excel sheet sample about experimental design.

Figure 7. Parametic B-pillar CAD model.

Figure 9. Thickness cloud of B-pillar hot forming result.

OPTIMIZATION OF HOT FORMING PROCESS USING DATA MINING TECHNIQUES

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process template is established and the thinning rate results is obtained in batch mode (Zheng et al., 2011). Taking the average among the 5 maximum values as the maximum thinning rate, the final database is shown in Table 3. Different heights on both sides of the B-pillar boss resulted in a height gradient. As shown in Figures 9 and 10, the rupture usually occurs where there is a height gradient, thus the gradient is marked as ‘Height” which is the observation object in the next DM analysis. In forming numerical simulation, there is a high probability of rupture if the TR of local zone is more than 20%. Therefore, the results of TR in the database are classified into “Dangerous” with TR exceeds 20% and “Safe” with TR equal to or below 20%, respectively. Table 3 shows the B-pilliar forming TR results and the corresponding classifications.

Figure 10. Local rupture of hot forming B-pillar.

3. DATA MINING FOR THE THINNING RATE RESULTS

Figure 11. Post-process template in HyperView.

maximum plastic strain of B-pillar hot forming result are the main observation objects. Typically, the Thinning Rate (TR) is extracted to analyze the rupture situation. As shown in Figure 9, the biggest TR occurs in the transition zone which means that local rupture usually occurs in this zone. This is confirmed by the actual test, as shown in Figure 10. Altair’s HyperWorks (HW) is a suite of engineering software platform, which provides many secondary development interfaces such as TCL/TK, C, and Java, etc. More importantly, HyperView, an important component of HW, is a post-process software package which provides automation functions with the Templex technology. According to the method realized in the reference, a post-

It’s difficult to build an accurate mathematical model to represent the correlation between the geometric size, forming parameters and the forming results, especially on the condition without knowing which parameters will affect the final forming result. The Decision Tree (DT) is a very useful and efficient algorithm in data mining, which requires no domain knowledge or special parameters setting. DT is suitable for detecting type of knowledge discovery,and its result can be described as a visual tree. In this paper, the DT was used to build the correlation between the forming parameters and forming results. 3.1. Brief Introduction of Decision Tree Algorithm The decision tree, which is based on divide and conquer algorithm, can classify data effectively. It classifies data according to the best attributes of data in every stage and then process every sub problem recursively in each category. Most of the current decision tree algorithms use topdown approach commonly and decision tress is constructed from the training sets and their associated class labels. Let D be the set of training tuples and corresponding class labels, attribute_list be the set of candidate attributes,

Table 3. Thinning rate results and classifications. o

o

ID

R (mm)

H1 (mm)

H2 (mm)

F (N)

BIT ( C)

TIT ( C)

TR (%)

Result

1

21.1

82.6

34.2

26969.7

600

48.7

15.6

Safe

2

9.0

81.8

30.4

12828.2

602.5

66.4

22.1

Dangerous

3

5.7

99.1

27.8

24545.4

605.0

60.4

25.8

Dangerous

…

…

…

…

…

…

…

…

…

99

29.4

90.3

30.7

42727.2

847.4

57.3

16.3

Safe

100

13.8

91.5

26.3

31414.1

850

68.4

16.5

Safe

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G. J. ZHENG, J. W. ZHANG, P. HU and D. Y. SHI

attrib_sel_method be the split criterion function method which returns the split criterion marked as splitting_criterion and corresponding split sub tuple marked as Dj(j = 1,2, 3…n), here is a part of the set and it satisfied the Equation (2). n

Dj = D ∑ j

(2)

=1

Figure 12 shows the basic algorithm flowchart of the DT generation function which was named Gen_Decision_Tree (D, attribute_list). Split criterion function can determine how to divide tuples into groups on given nodeswhich is the key to obtain good or bad decision tree result. C4.5 which is proposed by Quinlan is a standard supervised learning algorithm, and it obtains the information gain ratio as the split criteria. Equations (3) to (5) show the calculation process of the gain ratio. m

Entropy( D ) = –∑ pi log2( pi )

(3)

v D j Exception( A ) = ∑ ------- Entropy( Dj) D j=1

(4)

i=1

Entropy( D) – Exception( A ) GainRatio( A) = ------------------------------------------------------------------v D Dj j –∑ ------- log2⎛⎝ -------⎞⎠ D D

(5)

j=1

in which, D represents the number of total tuples,

Figure 13. Decision tree of the hot forming results. pi = Dj ⁄ D represents the probability of Dj in D . Tuples are divides into different groups according to the largest information gain ratio.

3.2. Data Mining According to the algorithm process shown in Figure 12 and taking information gain ratio as the splitting criterion, the forming results shown in Table 3 were classified to a decision tree. Waikato Environment for Knowledge Analysis (Weka) is a machine learning and data mining software, which is an open source environment based on JAVA language. Weka decision tree with parameter J48 –C 0.4 –M 5 was applied to analyze the hot forming results shown in Table 3. To improve the accuracy of the classification, a 10-fold cross-validation method was used and the final result was shown in Figure 13. Confusion matrix is used to reflect the classification result, where the rows represent the true classification and the columns represent the DT model classification. Table 4 shows the confusion matrix of the DT result shown in Figure 13. As shown in Table 4, 90 groups of data were classified correctly, while 10 groups were not. Here, six “Safe” groups were wrongly grouped into “Dangerous”, and four “Dangerous” groups were wrongly grouped into “Safe”. Therefore, the accuracy of this decision tress is about 90/ 100=90%.

4. RESULTS ANALYSIS As shown in Table 4, the accuracy of the DT classification Table 4. Confusion matrix of current DT.

Figure 12. Process of C4.5 algorithm.

Dangerous

Safe

Total

Correct rate

Dangerous

55

6

61

90.2%

Safe

4

35

39

89.7%

Total

59

41

100

90%

OPTIMIZATION OF HOT FORMING PROCESS USING DATA MINING TECHNIQUES

is 90% which is satisfactory for the current analysis. The following conclusions can be drawn through further analysis of the DT model. (1) There are 27 sets of “Dangerous” data when F (blankholder force) is bigger than 40204 N. This indicats that the blankholder force is a very important parameter for the hot forming process which should be lower than a certain value, otherwise the rupture occurs. (2) There are 15 sets of “Dangerous” data when F is lower than 40204N and Height is bigger than 66.9 mm. This indicats that the height gradient must not be too large, otherwise some serious ruptures will occur in the transition zone. So the height gradient of B-pillar must be taken into serious consideration in the structural design and die-face design. (3) There are 9 sets of “Dangerous” data when F is lower than 40204N, Height is lower than 66.94 mm and R is lower than 8.57mm. This indicats that rupture usually occurs on the hot forming of B-pillar when the fillet radius is too small. Bigger fillet radius will enhance the metal flowability between the die-faces because the transition zone with bigger fillet radius will be more smooth than the smaller one. From the decision tree result, the fillet radius is recommended to be bigger than 10 mm. (4) The initial temperature of sheet metal has a certain impact on the final forming result. As shown in the decision tree, the forming result is not satisfied if the initial temperature of sheet metal is higher than 712 C when the height gradient is more than a certain value (53.5 mm). The austenitizing temperature of the sheet metal is around 900 C, so the metal should be heated to about 900 C at first. Then the sheet metal temperature decreases quickly after it is put onto the die-face. Taking into account the actual situation in production, it is recommended that the sheet metal temperature should be controlled between 720 C to 800 C and the height gradient should be paid much attention to make the transition zone be as smooth as possible. (5) In actual hot forming process, there are many cooling channels inside the mould which can control the mould surface temperature in a certain range. From the result shown in Figure 13, the temperature of die-face does not affect the classification result, which means that the mould temperature in this small range do not significantly affect the final forming result. Thus a conclusion can be drawn from the experiment that if the die-face temperature can be controlled in a certain range, its influence upon the hot forming result can be neglected. In a word, in the hot forming process, a reasonable blankholder force must be chosen at first to make sure that the transition zone of the forming product be as smooth as possible which can be realized by using bigger fillet radius. Several reasons can be drawn for these conclusions: (1) The friction coefficient between the sheet metal and

die-face increased when the sheet metal was heated. Bigger friction coefficient means bigger tensile force with the same blankholder force. (2) It’s inconvenient to use lubricant between the the dieface and hot sheet metal. (3) Heating the sheet metal leads to lower yield strength and tensile strength; the former is benefitial for the metal flowability, while the latter arouse more rupture due to poor ability to resist tension which can cause local material thinning. When the thinning rate reached a certain value, then the rupture occurred.

5. VERIFICATION Based on the rules generated from the result analysis, a real B-pillar hot forming was performed by taking a group of recommended parameters and B-pillar geometry dimensions. The fillet radii are set to 12 mm and the height gradient is set

o

Figure 14. Thickness reduction of B-pillar.

o

o

o

335

o

Figure 15. Effective plastic strain of B-pillar.

Figure 16. Hot forming B-pillar product.

336

G. J. ZHENG, J. W. ZHANG, P. HU and D. Y. SHI

to 45 mm with the boss height being 70 mm and 25 mm, respectively. The blankholder force is set to 30000 N and the initial temperature of sheet metal is set to 750 C and the initial temperature of die-faces is set to 35 C. The FEM result is shown in Figure 14 and it has no appreciable thinning zone. The actual hot forming B-pillar product is shown in Figure 15 and it shows no rupture at all. The hot forming result indicates that the rules above have a positive and effective ability to guide the hot forming practice. o

o

6. CONCLUSION In this study, data mining and the FEM were used to look for the correlations between the forming process parameters, geometrical dimensions and the forming results of B-pillar hot forming. Some useful hot forming experiences were proposed for guiding the part design and hot forming simulation analysis. (1) The rules were based on data mining technology, extracted from a great number of hot forming simulation analysis and verified by a real B-pillar hot forming, which means that data mining technology is applicable for hot forming study. (2) Compared with cold forming, the design for the same parts in hot forming has special rules. The blank holder force must be less than that in cold forming. Meanwhile, the fillet radius should be larger in the transition zone and the height gradient should be smaller to make the transition zone more smooth. (3) It is strongly recommended that the initial temperature of the sheet metal should be controlled between 720 C to 800 C. At the same time, the temperature of the mould should be kept in a small range. The following aspects can be taken into account in the future work: (1) Some forming parameters which are also related to the hot forming result are not taken into account in this paper, such as the punch velocity and the quenching speed. Next we will examine more forming parameters for hot forming result and do some detailed comparison with cold forming. (2) The crashworthiness of the hot forming product is not taken into account after the forming process. Currently, the hot forming is mainly used for structural safety components in automobile and the crashworthiness is not only releated to the yield stress and tensile strength, but also the geometric shape and size. Thus our next work will consider the relationship of the forming parameters and crashworthiness. o

o

ACKNOWLEDGEMENT−This work founded by the “Fundamental Research Funds for the Central Universities of China (Grant Nos. 3013-852013)” and the Key Project of the National Natural Science Foundation of China (No. 10932003, 11272075). These supports are gratefully acknowledged. Many thanks are due to the referees for their valuable comments.

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OPTIMIZATION OF HOT FORMING PROCESS USING DATA MINING TECHNIQUES

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