A Study on the Optimal Design of Automobile Interior

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2009-01-1232

A Study on the Optimal Design of Automobile Interior Plastic Parts (A-Pillar Trim) Considering

Heat-Resistant and Mechanical Characteristics

Hyunjun Kim, Hoon Cho and Youngtak Son Sungkyunkwan University

Seungsoo Ryu, Haeryong Kim and Hunsoo Kim

Myungwon Suh

Copyright © 2009 SAE International

ABSTRACT

Interior parts that are composed of plastic usually deform under various temperature conditions. It is necessary to obtain the material properties for an analysis of the thermal deformation under the heat cycle test. Specifically, creep data of plastic material was introduced for studying the time-dependent deformational behavior of the pillar trim in the heat cycle test. The time-hardening version of the power-law creep model was applied to account for the permanent deformation following the heat cycle test, which was verified through a comparison of the test results with the result of finite-element analysis for a simple model. In this study, a methodology was developed for the optimal design of the A-pillar trim in terms of the positions of the mounts. The analyzed results were used to approximate a function that was constructed by the response-surface method. Design procedures were repeated to minimize the thermal deformation at the areas of interest. We also developed a methodology for designing the rib pattern of A-pillar trims. Nonlinear finite element analysis has been implemented and integrated with a method of sensitivity analysis for minimizing the thermal deformation at the areas of interest.

INTRODUCTION

Most automobile interior parts consist of plastic components. These components must satisfy several criteria, including the thermal-cycle resistance, vibration resistance, and impact resistance. The automobile industry is working to reduce the thermal deformation that occurs through periodical, seasonal changes. Of late, these efforts have culminated in a plan to reduce thermal deformation and increase the marketability of product in overseas markets.

To predict the thermal deformation, it is customary to perform an experiment by using a test vehicle and to conduct simulation by running a finite-element analysis program on a computer. Nowadays, the movement of vehicle components under constraints can be predicted by the rapid development of computing power and the continuing advances in the methodology for analysis. Also, studies of plastic deformation are underway in a variety of ways. Choi[1] derived the residual stress through the injection-molding analysis of a plastic fender, and elaborated the means of predicting the thermal deformation by the assembly of the product that is undergoing the stress. Using two-dimensional, triangular elements, Yang[2] studied the strain,

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development of thermal stress, and deformation, which arise from the cooling of an injection-molded product within the mold.

By using three-dimensional, tetrahedral elements, Park[3] conducted an analysis of the residual stress and strain of injection-molded product. These studies had limitations with regard to the prediction of the movement of material[4], such as plastic, which experiences large variations in the mechanical properties with the temperature. The reasons for the limitations are that these studies involve analytical methods that predict the residual stress in injection-molded product and that the theoretical approach for analyzing the thermal strain is based on a mathematical model about material movement.[5]

In this study, we acquired data on material properties by performing a tensile test and a creep test, and by measuring the coefficient of linear expansion. Using these data on material properties, we defined the process of analysis for predicting the thermal strain. Through this process, in this study, we suggest a method of optimizing the reduction in the thermal strain.

HEAT CYCLE TEST

The following heat-cycle gives us the conditions of the experiment and sequentially describes the heat-resistance test, the cold-resistance test, and the wet-resistance test.

Each procedure is as follows.

The test for ascertaining the properties of the heat

cycle mentioned in section 1 involves three iterations of the heat cycle, as shown in Figure 1. We can evaluate compatibility by applying the criteria of generated displacement.

Figure 1 Conditions of the heat cycle test

FUNDAMENTAL EXPERIMENT AND CREEP MODEL

The front-pillar trim, which is the relevant component in this study, is Polypropylene with 20% talc. The heat-resistant properties are manifested during the heat cycle test. For developing an analytical method that corresponds to Figure 1, the heat cycle and material properties that are appropriate to each range of temperature are needed. For acquiring such data in this study, we divided the overall region into a transient region and a steady-state region and then acquired data on properties. In other words, for acquiring the elastic and plastic properties, both the tensile test and the measurement of the coefficient of linear expansion are executed in the transient region. For acquiring creep data of the steady-state region, a winding creep test was performed.

CREEP MODEL

In this study, for applying the winding creep data that are acquired as reported in subsection, the behavior of creep is mathematically expressed by using the time-hardening version of the power-law creep that is appropriate to the static load condition.

1. In the heat-resistance test, the temperature of the atmosphere in the chamber rises up to 80℃ from 23℃. After we maintain the high temperature by using a light bulb or a lamp, we take down the temperature to 23℃.

2. The cold-resistance test starts at the normal temperature of 23℃ and rises back to the normal temperature after descending to -40℃.

3. In the wet-resistance test, the temperature is 50℃ and the relative humidity is 90%. After maintaining such conditions, we let the temperature of the chamber come back to the normal temperature.

The tensile test was performed by using the specimen, ASTM D638 NO.1. Both Figure 2 and Table 1 explain the main properties that are to be acquired through the tensile test. Since the main loading condition of the experiment that is relevant to the heat cycle test is the temperature, the coefficient of linear expansion, which explains the variation of the length per unit length owing to the temperature, is measured and expressed as in Figure 3. Finally, the winding creep test is performed for acquiring data on properties of the steady-state region. In line with ASTM D2990, the winding creep test is performed with respect to three loads under diverse temperatures (23℃, 50℃, 90℃, and 100℃).

Figure 4 describes the experimental equipment for the winding creep test. Figure 5 describes the result for a temperature of 100℃.




mncreep tAσε = (1)

In Eq. (1), creepε is the creep strain rate, σ is

suitability variation stress and t is the time

Table 1 Mechanical properties of the specimen

Temperature Tensile strength (MPa)

Yield strength (MPa)

E (GPa) υ

(Poisson’ s ratio)

-40℃ 52.4 43.8 7.060 0.3450℃ 26.9 15.5 2.174 0.4790℃ 19.2 11.4 1.413 0.52

100℃ 15.9 9.8 1.216 0.54

Figure 2 Equipment for the tensile test

Figure 3 Thermal expansion curve of the specimen

Figure 4 Apparatus for the flexural creep test of

plastic material

Figure 5 Results of the creep test under a

temperature of 100℃

In Eq. (1), the coefficients to be obtained, namely, A, n, and m, are derived from the nonlinear curve that fits the experimental data of the creep test. These coefficient values have to meet the following conditions: both A and n must be positive numbers and m must be a real number between -1 and 0. Table 2 shown material properties for heat-transfer analysis.

ANALYSIS OF THE THERMAL DISPLACEMENT

In this section, as a prerequisite for developing a process for reducing the thermal displacement, we analyze the thermal displacement for the front-pillar trim and examine the appropriateness of the process of analysis through a comparison with the experimental results of the real car.




FINITE ELEMENT MODEL

The model for analysis is a front-pillar trim that is composed of 30 ribs and 3 mounts. The mesh of the FE model is generated by using the Hypermesh[6]. Figure 6 shows the FE model that is generated. The number of elements is 3,691. The number of nodes is 1,874. As expressed in the following figure (Figure 7), the boundary conditions entail fixing: the translational motion for the three mount; the perpendicular displacement of the element that is in contact with the chassis; and the perpendicular displacement of the element that is in contact with glass

Figure 6 Finite-element model of the A-pillar trim

Figure 7 Loads and boundary conditions

The loading conditions include a thermal load for the thermal cycle and a load for contact with the weather strip and the headliner. The FE model is made up 3-node shell elements. The program for analysis is ABAQUS Version 6.5[7].

FINITE ELEMENT ANALYSIS

Figure 8 depicts a flowchart that roughly expresses the process of analysis of the thermal displacement. The process of analysis is segmented into heat-transfer analysis for acquiring the temperature distribution and heat-stress analysis for acquiring the distributions of the displacement and the stress. In other words, we acquire the temperature distribution of the whole FE model and the data that are used to analyze the heat transfer. The heat-stress analysis is completed by repeating the static analysis for the transient-state of the thermal cycle and the creep analysis for the steady-state. Figure 9 illustrates the results of the experiment on the real car. Figure 10 presents the result, which is obtained from FE analysis, on the displacement of the region of interest. There is the difference of pillar trim for displacement of headliner from displacement of contiguity in headliner. However, the overall form of displacement is very similar.

Table 2 Material properties for heat-transfer analysis conductivity

(W/m ⋅ ℃)

specific heat

(J/kg ⋅ ℃)

density

(kg/m3)

0.25 1,932 1,040

Figure 8 Flowchart of the procedure for analysis




Figure 9 Experimental result (Real Car)

Figure 10 Result of the analysis

RIB-PATTERN DESIGN CONCERNING THE THERMAL DISPLACEMENT

For developing the methodology for reducing the thermal displacement, based on the advice of a designer who has had considerable experience in the design of pillar trims, we treat the rib pattern as the design variable. The process of designing the rib pattern is described in Figure 11.

Figure 11 Flowchart of the rib-pattern design

process

We can generate a model for alternating the rib pattern by using a program that is developed on the basis of the Hypermesh that is used in this study. Using the results of analysis for the model that is generated as shown in Figure 12, we decide the appropriate interval of the rib.

Figure 12 An example of rib-mesh generation (10mm)

After performing sensitivity analysis for each rib for

the displacement in the region of interest, we can acquire a report for explaining the sensitivity of each rib, as shown in Figure 13. After we remove those ribs that do not affect the displacement of the region of interest, we acquire a rib pattern that is similar to that shown in Figure 14. For the current and new models, Table 3 describes the displacement of the region of interest and




the maximum displacement of the overall model. Through these results, we confirmed the suitability of the methodology for the present study.

Figure 13 Result of sensitivity analysis

Figure 14 The final rib pattern

Table 3 Comparison of the thermal deformation between the current and new models

Model Deformation of the area of interest

Maximum deformation

Current 1.378 5.887New 0.957 (-30.55%) 5.592 (-5.01%)

OPTIMIZATION OF THE LOCATION OF THE MOUNT

Figure 15 describes the process of optimization that is suggested in this study. Based on the advice of a designer who has had considerable experience in the

design of pillar trims, we consider the design variable to be the locations of three mounts. The factors are the locations of mounts, as depicted in Figure 16. The levels are described in Table 4. The objective function is the sum of displacements, as shown in Figure 16. Moving direction of mount is long way of pillar.

We simulate 27 models by applying a full factorial design for 3 factors and 3 levels. Table 5 describes the displacement that is derived from analysis.

Figure 15 Flowchart of a methodology for the optimal

design of the mount position

Figure 16 Model for finite-element analysis




Table 4 Factors and levels Factor Level 1 Level 2 Level 3

A -20 mm -10 mm 0 mm

B -10 mm 85 mm 180 mm

C -50 mm 20 mm 90 mm

Table 5 Full factorial table and results

No A B C Disp. in the

area of interest (mm)

Maximum disp. (mm)

1 -20 -10 -50 5.3383 6.887

2 -20 -10 20 5.8660 9.908

3 -20 -10 90 5.4645 14.190

4 -20 85 -50 4.0581 6.455

5 -20 85 20 4.8492 6.900

6 -20 85 90 4.6045 11.800

7 -20 180 -50 3.5670 7.818

8 -20 180 20 3.7244 7.292

9 -20 180 90 3.8671 10.490

10 -10 -10 -50 5.2369 6.879

11 -10 -10 20 5.8102 9.710

12 -10 -10 90 5.5716 14.080

13 -10 85 -50 3.9407 6.577

14 -10 85 20 4.3662 7.071

15 -10 85 90 4.4533 11.650

16 -10 180 -50 3.3336 8.267

17 -10 180 20 3.3491 7.481

18 -10 180 90 3.6566 10.420

19 0 -10 -50 5.2973 7.064

20 0 -10 20 5.9401 9.545

21 0 -10 90 5.6369 13.850

22 0 85 -50 3.8672 6.841

23 0 85 20 4.3874 7.012

24 0 85 90 4.5004 11.470

25 0 180 -50 3.3134 8.615

26 0 180 20 3.4856 7.444

27 0 180 90 3.6091 10.350

The regression function that is derived by using the values in Table 5 is presented in Eq. (2). The R-squared value of the regression function is 0.97, which means the regression function is reliable.

322764.13115618.021031592.02

3374283.122263983.12

108895.0

3572694.2278844.1104726.07804.11

XXXX

XXXXX

XXXY

−−

++++

+−−=

(2)

The variables 321 ,, XXX that are used in the

regression function are changed to the scaled values by

using Eq. (3). The equation that relates CBA ,, (the real values of the translation of mounts) and 321 ,, XXX is as

follows (Eq. (4)).

3,,1,)()(

})(){(2L=⎟

⎟⎠

⎞⎜⎜⎝

⎛

+

+−= i

xxxxx

Xloweriupperi

loweriupperiii

(3)

Where, Xi is ,X1, X2, X3 and Xiupper is upper boundary of X1, X2, X3 and Xilower is lower boundary of X1, X2, X3.

20370

85295

10110

+=

+=

−=

XC

XB

XA

(4)

As with Eq. (2), the regression function is a simple mathematical model. Hence, by using mathematical optimization techniques, we acquire the following.

8253.03,3162.02,5163.01 −==−= XXX

The above values are changed to the following values by using Eq. (4).

771.37,039.115,163.15 −==−= CBA

The physical meaning of the above values is that each A and C mount is relocated downwards from the existing locations by 15.163mm and 37.771mm, respectively, and the B mount is relocated upwards from the existing location by 115.039mm.

Table 6 compares the result of the regression function with the results of analysis, with regard to the optimal values. The values in parentheses describe the percentage reduction with reference to the displacement of the original model. The error between the result of the regression function and the result of analysis is 2.3%, which implies that the regression function is reliable.




Table 6 Final result Original

model Regression

function Analysis

resultDisp. of interest 5.958 3.893

(34.6%) 4.098

(31.2%)Maximum disp. 8.674 6.555

(24.4%) 6.595

(24.0%)Disp. of interest

+ Maximum disp

14.632 10.448 (28.6%)

10.692 (26.9%)

CONCLUSION

In this study, we conducted fundamental experiments (heat cycle test, creep test, tensile test, etc.) and finite element analysis for predicting the thermal deformation of A-pillar trims. Next, we developed a design process for reducing the empirical thermal deformation.

This research has the following conclusions.

(1) We acquired the data on material properties that are relevant to the thermal cycle and confirmed that the result of the analysis of thermal displacement approximately conformed to the experimental result of a real car (the error was within 5%).

(2) Through computer simulation and an experiment with a real car, we developed the process of design for reducing the thermal displacement. We confirmed that these results can be applied to front-pillar trims. The displacement of the optimal model is reduced by 10% when compared to the displacement of the existing model.

(3) We confirmed that the total displacement of the optimal model is reduced by 28.6%, as compared with the displacement of the existing model, as the result of the optimization of the mount positions.

(4) By computerizing the design process for relying on experience and exploiting techniques of optimization, we laid the foundation for a systematic method of design..

ACKNOWLEDGMENTS

This work was supported by NGVTEK funded by HYUNDAI-KIA MOTORS.

REFERENCES

1. S. S. Yang and T. H. Kwon, "Deformation analysis of injection molded articles due to in-mold residual stress and subsequent cooling after ejection", transaction of the KSME(A), Vol. 26, No. 2, pp. 240-348, 2002.

2. K. Park, J. H. Ahn and C. H. Yim, "Residual stress estimation and deformation analysis for injection molded plastic parts using three-dimensional solid elements", transaction of the KSME(A), Vol. 27, No. 4, pp. 507-514, 2003.

3. H. C. Lee, H. M. Park, S. H. Ji, I. K. Jang, "The optimal rib design considering thermal deformation and dynamic stiffness of automotive interior pillar trim", spring conference proceedings of the KSAE, pp. 1163-1168, 2006.

4. H. Y. Kim, J. J. Kim, J. S. Kim, "A study on the warpage and post-deformation in heat resistance test of automotive plastic components", Journal of the Korean society of precision engineering, Vol. 13, No. 5, pp. 44-52, 1996.

5. K. H. Yoon, "Plastics in automotive components", Advanced materials and manufacturing in automotive engineering, No. 2, pp. 33-38, 2006.

6. Hypermesh User's manual, Altair, 2006. 7. ABAQUS User's manual 6.5, HKS, Inc. CONTACT

MYUNG-WON SUH (Corresponding author)

Professor / School of Mechanical Engineering / Sungkyunkwan University

300 Chunchun-dong, Jangan-gu, Suwon, 440-746, South Korea

Phone: +82-31-290-7447 Fax: +82-31-290-7447

E-mail: [email protected]




A Study on the Optimal Design of Automobile Interior

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