摘要
論文題目(中文)：應用內隱與外顯式有限元素法於車輛輪胎水漂性能及防撞結構安全防護之研究
論文題目(英文)：A Study of Automotive Aquaplaning Behavior and Structural Crashworthiness Performance Using Explicit/Implicit Finite Element Methods
指導教授：鄭泗滄 教授

本文主旨是利用內隱與外顯式有限元素法進行車輛輪胎水漂性能及防撞結構安全防護的研究，並透過實驗與對照參考文獻數據的方式，來驗證有限元素模型的正確性，進而設計並發展出能增加輪胎的排水性能的花紋以及提升防撞管件結構吸收能量的觸發機構。
對於車輛輪胎水漂性能方面，本文主要在於研究多種花紋(光頭花紋、直排花紋、V型花紋)的先進複合材料輪胎的排水性行為。本文將輪胎結構中的複合材料補強層與花紋或胎邊，分別使用古典基層板理論(Classical Laminated Theory, CLT)與Mooney-Rivlin模型，來描述等效材料性質。而Arbitrary Lagrangian-Eulerian (ALE)方法,則用於模擬輪胎在經過積水路面複雜的流固耦合(Fluid Structure Interaction, FSI)現象。
在靜態壓縮模擬與實驗方面，本文透過靜態壓縮實驗數據與FEM模型驗證，其反力與壓印面積的誤差都在10%以內。在數值驗證方面，本文使用LS-DYNA與Nakajima等人，比較輪胎滾動在乾地路面時的正向接觸反力， 與DYTRAN模擬結果比較正向反力曲線，都有相當一致的結果。而對於排水性能驗證方面，本文與Okano與Koishi等人比較光頭、直排與V型花紋的輪胎(195/65R15)，排水性能的誤差都在可以接受的範圍之內。而對於直排花紋輪胎而言，本文將探討不同的主溝寬度、不同的深度積水路面、不同軟硬程度的花紋、不同的花紋區間以及不同個數的主溝花紋對輪胎排水性能的影響。而對於V型花紋輪胎而言，本文將探討正轉與反轉的差異、不同角度的特徵角、不同個數的特徵花紋以及24°前緣傾斜角對於輪胎排水性能的影響。最後，透過將V型花紋與直排花紋的幾合特徵結合，發展出能提升40.2%的輪胎排水速度(Tire hydroplaning velocity)的輪胎花紋。
對於防撞結構安全防護方面，本文主要在於研究金屬管件的靜動態衝壓潰縮行為。由於管件結構常用於汽車防撞設計中，本文將金屬管件結構中加入不同的觸發機構(Triggering mechanisms)，來提升管件結構的吸收能量效果，並且減低初始衝擊力的大小。在衝擊壓縮模擬中，金屬管件使用Power Law Plasticity模型與Elasto-Plastic模型，並且考慮應變率效應的影響。而在實驗與數值擬靜態驗證方面，本文使用LS-DYNA與Seitzberger等人以及Santosa等人，比較空心金屬管件或含泡綿金屬管件的初始衝擊力、平均力與吸收能量，都有相當一致的結果。此外，本文也將探討不同的孔洞大小、不同的孔洞形狀、不同壓印深度的金屬管件對防撞金屬管件結構的潰縮性能影響。而在數值動態模擬驗證方面，本文使用LS-DYNA與Ghasemnejad等人，比較空心金屬管件與含皺紋狀金屬管件的初始衝擊力、動態平均力與吸收能量，都有相當一致的結果。
而在解析模型方面，透過Ghasemnejad發展對含皺紋狀金屬管件的理論解析模型，本文加入凸狀觸發機制，去引導金屬管件在潰縮過程中，不斷使空心管件結構產生延展皺摺模式(extensional mode)，進而發展出新的解析模型，透過數值與模擬的比較，其誤差都在可接受的範圍內。並且此種設計，在對於含凸狀觸發機制且為最小間距的皺紋狀金屬管件，可提升74%的吸收能量效果以及降低75%的初始衝擊力。

ABSTRACT
A Study of Automotive Aquaplaning Behavior and Structural Crashworthiness Performance Using Explicit/Implicit Finite Element Methods

Student: Yuen-Sheng Chiu
Advisor: Syh-Tsang Jenq

The purpose of this study concerns with automotive aquaplaning (i.e. hydroplaning) behavior and structural crashworthiness performance using explicit/implicit finite element methods. Parts of current simulations for advanced radial tires and thin-walled square tubes resemble test determined results and/or previous studies. Current numerical scheme in LS-DYNA is adequate and accurate to analyze these specific characteristics due to corresponding verifications in the present work. Investigations of specific tread patterns and triggering mechanisms for tire and tube structures were, respectively, developed to enhance hydroplaning performance and energy-absorption capability.
Three types of tread patterns (i.e. smooth, longitudinally-grooved and V-shape grooved patterns) for the inflated radial tires were examined to understand their hydroplaning performances in the current work. The Mooney-Rivlin constitutive law and classical laminated theory (CLT) were used to depict the mechanical behaviors of rubber material and composite reinforcing layers, respectively. The Arbitrary Lagrangian & Eulerian (ALE) formulation was adopted to describe the fluid-structure interaction between tire structure and fluid/void film. The quasi-staticlly compressed numerical results for the inflated tire were in good agreements with test results. Due to the verification of dynamic rolling behavior, the current numerical relationship of normal contact force and operational time was corresponded with that of Nakajima’s study for the inflated smooth tread pattern tire. In order to further check against hydroplaning behavior for the tire, insignificant difference of hydroplaning performances for 195/65R15 tires with smooth, V-shape and longitudinally-grooved tread patterns were reported when compared with Okano and Koishi’s test results in the current work. Effects on hydroplaning velocity of groove width, water film depth, rigid/soft tread patterns, groove spacing and groove number for longitudinally-grooved tread pattern tires were presented. In addition, effects on hydroplaning performance of normal/reverse rotations, pitch angle, pitch number, groove spacing and an inclined front nose for V-shape grooved tread pattern tires were also discussed. After combining the longitudinally-grooved tread pattern tire with an inclined front nose, a 40.2% increase of tire hydroplaning velocity was reported when compared with that of smooth tread pattern tire.
With regard to the structural crashworthiness, crushing characteristics of metallic thin-walled square tubes with triggering mechanisms under quasi-static and impact loads were studied. Triggering mechanisms were found to improve energy-absorption capability and initial peak force for tube structures. The power law plasticity strain hardening and elasto-plastic material models considering strain rate effect in LS-DYNA were utilized to describe dynamic stress-strain relationship for metallic thin-walled tubes in question. Good agreements of initial peak force, dynamic mean force and energy-absorption capability between current FE results and Seitzberger’s test results for the thin-walled square tubes with and without foam core materials were reported. Effects on crushing characteristics of discontinuities size, discontinuities shape and pre-indented wall surface were also examined for metallic thin-walled square tubes under quasi-static loading. In addition, insignificant differences of initial peak force, dynamic mean crushing force and specific energy absorption for corrugated thin-walled tubes subjected to an impact loading were presented when compared with that of Ghasemnejad’s study.
The theoretical model of corrugated thin-walled tube was reported by Ghasemnejad. An important design concept of current modified theoretical model was proposed to induce the extensional deformed mode by joining bulging mechanisms for the corrugated thin-walled tube model. Good agreements of dynamic mean force between theoretical model and present simulated analysis for modified corrugated thin-walled tubes were reported. This proposed design (i.e. with bulging mechanisms) was effective to significantly enhance 74% specific energy absorption and decrease 75% initial peak force for the corrugated thin-walled tube containing bulging mechanisms with a minimum pitch distance.

An, J. C. and Cho, J. R., 2008. “Tire Standing Wave Simulation by 3-D Explicit Finite Element Method,” ICCES, v. 7(3), pp. 123-128.

Allbert, B.J., 1968. “Tires and Hydroplaning”, SAE Paper No. 680140.

Belytschko, T., Guo, Y., Liu, W. K. and Xiao, S. P., 2000. “A Unified Stability Analysis of Meshless Particle Methods,” International Journal for Numerical Methods in Engineering, v. 48 (9), pp. 1359-1400.

Clough, R. W., 1960. “The Finite Element in Plane Stress Analysis,” Proceedings, 2nd ASCE Conference on Electronic Computation, Pittsburgh, Pa.

Clark, S. K., 1981. Mechanics of Pneumatic Tires, US Department of Transportation, Washington, DC, USA.

Chiu, Yuen-Sheng, 2008. A Study of the Dynamic Rolling Contact Behavior and Tread Pattern on Hydroplaning for Commercial Automotive Tires, MS thesis (advisor: Prof. Syh-Tsang Jenq), Department of Aeronautics and Astronautics, National Cheng Kung University, Taiwan.

Chiu, Y. S. and Jenq, S. T., 2013. “Crushing Behavior of Metallic Thin-wall Tubes with Triggering Mechanisms due to Quasi-static Axial Compression,” Journal of the Chinese Institute of Engineers (JCIE). (accepted)

Chopra, Anil K., 1995. Dynamics of Structures : Theory and Applications to Earthquake Engineering, Prentice-Hall Inc, Englewood Cliffs, New Jersey, USA.

Courant, R.; Friedrichs, K.; Lewy, H., 1928. “On the Partial Difference Equations of Mathematical Physics,” IBM Journal of Research and Development, v.11(2), pp. 215-234.

Fox, R. W., McDonald, A. T., Pritchard, P. J., 2004., Introduction to Fluid Mechanics, 6th Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA.

FLOTREND Corporation, 2006. LS-DYNA Implicit/Explicit Technique Course, Taipei, Taiwan, R.O.C..

Grogger, H. and Weiss, M., 1996. “Calculation of the Three-Dimensional Free Surface Flow Around and Automobile Tire,” Tire Science and Technology TSTCA, v. 24(1), pp. 39-49.

Grogger, H. and Weiss, M., 1997. “Calculation of the Hydroplaning of a Deformable Smooth-Shaped and Longitudinally-Grooved Tire,” Tire Science and Technology TSTCA, v. 25(4), pp. 265-287.

Ghasemnejad, H., Hadavinia, H., Marchant, D. and Aboutorabi, A., 2008. “Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing,” SDHM: Structural Durability & Health Monitoring, v. 4, pp. 29-45.

Ghoreishy, M. H. R., 2006. “Steady State Rolling Analysis of a Radial Tyre: Comparison with Experimental Results,” Journal of Automobile Engineering, v. 220(6), pp. 713-721.

Germund, Dahlquist et al., 1974. Numerical Method, Prentice Hall, Englewood Cliffs, New Jersey, USA.

Hallquist, J. O., 1998. LS-DYNA Theory Manual, Livermore, v.971, pp.2.15-2.21.

Hallquist, J. O., 2007. LS-DYNA Keyword User’s Manual, Livermore, v.971, pp.128-130 (MAT).

Ei-Hage, H., Mallick, P. K. and Zamani, N., 2005. “A Numerical Study on the Quasi-static Axial Crush Characteristic of Square Aluminum Tubes with Chamfering and Other Triggering Mechanisms,” International Journal of Crashworthiness, v. 10(2), pp. 183-196.

Jenq, S. T., Ting, Y. C., Liang, S. M., Lin, D. and Shih, M., 2008. “Quasi-static Compression and Rolling Contact Analysis of MAXXIS VICTRA MA-Z1 Tire on Dry Roadway,” International Journal of Modern Physics B, v. 22(9/11), pp. 1531-1537.

Jenq, S. T. and Chiu, Y. S., 2009. “Hydroplaning Analysis for Tire Rolling over Water Film with Various Thicknesses Using the LS-DYNA Fluid-Structure Interactive Scheme,” Computers, Materials & Continua (CMC), v. 11(1), pp. 33-58.

Jones, N., 1993. Structural Impact, Cambridge University Press, Cambridge, UK.

Jenq, Syh-Tsang, Chiu, Yuen-Sheng and Wu, Wen-Jie, 2011. “Transient Hydroplaning Performance Analysis for Inflated Chevron Grooved Tires with Various Pitch Angle,” 35th National Conference on Theoretical and Applied Mechanics, pp. 1015, Tainan, Taiwan, 18-19 November.

Jenq, S. T., Hsiao, F. B., Lin, I. C., Zimcik, D. G. and M. Nejad Ensan, 2007. “Simulation of a Rigid Plate Hit by a Cylindrical Hemi-spherical Tip-ended Soft Impactor," Computational Materials Science, v. 39(3), pp. 518-526.

Jenq, S. T., Chiu, Y. S., Ting, Y. C. and Chu, Chuck, 2008. “Dynamic Contact Rolling Analysis for Tires with Smooth and Longitudinal grooved Tread Patterns Passing a Speed Bump Obstacle,” 3rd International Symposium on Advanced Fluid/Solid Science and Technology in Experimental Mechanics, pp. 95, 7-10 December, Tainan, Taiwan.

Jenq, S. T., Chiu, Y. S. and Ting, Y. C., 2008. “Transient Hydroplaning Simulation of Automotive Tires Using the Fluid-Structure Interaction FEM Method,” 9th International Conference on Computational & Experimental Engineering and Science, pp. 139, 8-13 April, Phuket, Thailand.

Jenq, Syh-Tsang and Chiu, Yuen-Sheng, 2011. “Verification and Analysis of Transient Hydroplaning Performance for inflated Radial Tire with V-shaped Groove Tread Pattern on the Fluid Structure Interaction Scheme,” 11th International Conference on Computational & Experimental Engineering and Science, pp. 27, 17-21 April, Nanjing, China.

Jenq, Syh-Tsang, Chiu, Yuen-Sheng and Wu, Wen-Jie, 2012 “Verification and Analysis of Transient Hydroplaning Performance for Inflated Radial Tire with V-shaped &Proto-type Grooved Tread Pattern Using LS-DYNA Explicit Interactive FSI Scheme,” 7th International Symposium on Advanced Science and Technology in Experimental Mechanics (7th ISEM'12), Paper no. B102, 08-11 November, Hsinchu, Taiwan.

Jenq, S. T. and Chiu, Y. S., 2013 “Transient Hydroplaning Performance of Inflated Radial Tire with V-shape Grooved Tread Pattern Using LS-DYNA Explicit Interactive FSI Scheme,” Journal of the Chinese Society of Mechanical Engineers (CSME). (accepted)

Jones, N., 1993. Structural Impact, Cambridge University Press, Cambridge, UK (pp. 405-406)

Langseth, M. and Hopperstad, O. S., 1996. “Static and Dynamic Axial Crushing of Square Thin-Walled Aluminum Extrusions,” International Journal of Impact Engineering, v. 18, pp. 949-968.

Meguid, S. A., Heyerman, J. and Stranart, J. C., 2002. “Finite Element Modeling of the Axial Collapse of Foam-Filled Structure,” Journal of Spacecraft and Rockets, v. 39, pp. 828-832.

Nakajima, Y., Seta E., Kamegawa, T. and Ogawa, H., 2000. “Hydroplaning Analysis by FEM and FVM: Effect of Tire Rolling and Tire Pattern on Hydroplaning,” International Journal of Automotive Technology, v. 1(1), pp. 26-34.

Okano, T. and Koishi, M., 2001. “A New Computational Procedure to Predict Transient Hydroplaning Performance of a Tire,” Tire Science and Technology TSTCA, v. 29(1), pp. 2-22.

Ogden, R. W., 1986. “Recent Advances in the Phenomenological Theory of Rubber Elasticity,” Rubber Chemistry and Technology, v. 59, pp.361-382.

Pacejka, B. Hans, 2006. Tire and Vehicle Dynamics, Second Edition, Society of Automotive Engineers, Inc., Warrendale, PA.

Qingwu, Chenga, William, Altenhofa and Li, Lib, 2006. “Experimental Investigations on the Crush Behavior of AA6061-T6 Aluminum Square Tubes with Different Types of Through-hole Discontinuities,” Thin-walled Structures, v. 44, pp. 441-454.

Reaz, Ahmed S. and Deb, Nath S. K., 2009. “A Simplified Analysis of the Tire-tread Contact Problem Using Displacement Potential Based Finite-difference Technique,” Computer Modeling and Engineering Science, v. 44(1), pp. 35-63.

Ray, W. Clough and Joseph, Penzien, 1993. Dynamics of Structures, Second Edition, McGraw-Hill International, Inc., New York, USA.

Ronald, F. Gibson, 2007. Principles of Composite Material Mechanics, Second Edition, Taylor & Francis Group , LLC , Boca Raton, USA.

Seitzberger, M., Rammerstorfer, F. G., Degischer, H. P., Vienna, and Gradinger, R., 1997. “Crushing of Axially Compressed Steel Tubes Filled with Aluminum Foam,” Acta Mechanica, v. 125, pp. 93-105.

Sigit, P. Santosa, Tomasz, Wierzbicki, Arve, G. Hannssen and Magnus, Langseth, 2000. “Experimental and Numerical Studies of Foam-filled Sections,” International Journal of Impact Engineering, v. 24, pp. 509-534.

Sivakumar, Palanivelu et al, 2010. “Comparison of the Crushing Performance of Hollow and Foam-filled Small-scale Composite Tubes with Different Geometrical Shapes for Use in Sacrificial,” v. 41 Part B, pp. 434-445.

Ting, Yu-Cheng, 2006. A Study of the Quasi-static Compression Behavior and the Dynamic Rolling Response for Advanced Automobile Tires, MS thesis, Department of Aeronautics and Astronautics, National Cheng Kung University, Taiwan.

Timoshenko, S. P., 1953. History of Strength of Materials, McGraw-Hill Book Company, New York, USA.

Wierzbicki, T. and Abramowicz, W., 1983. “On the Crushing Mechanics of Thin-walled Structure,” Journal of Applied Mechanics, v. 50, pp. 727-734.

Yang, T. Y., 1986. Finite Element Structural Analysis, Englewood Cliffs, N.J., Prentice-Hall, USA.