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研究生: 陳伽達
Chen, Qie-Da
論文名稱: 生物組織之軟彈液動潤滑分析
Soft-Elastohydrodynamic Lubrication Analysis on Biotissues
指導教授: 李旺龍
Li, Wang-Long
學位類別: 博士
Doctor
系所名稱: 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年: 2020
畢業學年度: 108
語文別: 中文
論文頁數: 102
中文關鍵詞: 軟彈液動潤滑生物軟組織橫向等向性材料
外文關鍵詞: Soft-EHL, Biological Tissues, Transverse Isotropic Material
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  • 軟彈液動潤滑是生物磨潤系統中非常重要的問題,軟組織藉由有限的大變形來減少相對運動的表面之間的摩擦和破壞。傳統(硬)彈液動與軟彈液動潤滑的數值計算方法存在著些差異,傳統彈液動缺乏將“軟”的關鍵特徵考慮在數值計算的模型分析。
    本文將建立軟彈液動潤滑的線接觸模型的數值計算方法,材料尺寸以有限厚度取代彈性半空間假設並考慮材料幾何非線性及有限應變理論。流體表面速度則考慮受到材料有限變形引起的曲率效應。數值計算是藉由有限元素法分析各種表面夾帶速度、材料楊氏係數及不同條件參數下討論流體壓力、流體薄膜厚度和材料變形及應力分布。在軟彈液動潤滑和硬彈液動潤滑建模假設進行比較,之後再考慮生物軟組織的橫向等向性的特性,在各種楊氏係數及蒲松比的組合下,討論流體壓力、流體薄膜厚度和材料的變形及應力分布,獲得橫向等向性材料最佳的參數組合。
    分析結果表明傳統彈液動潤滑不適用於高負載及低楊氏係數材料,軟彈液動潤滑模型更符合現實的結果。在接觸區域中,傳統彈液動計算模型會高估壓力分佈而低估膜厚和變形,軟彈液動潤滑模型具有更平緩的應力分佈。因此,本研究所建立的軟彈液動潤滑模型能幫助軟材料在設計上的參考依據。

    Soft elastohydrodynamic lubrication (soft-EHL) is an important topic in the biotribological system. The finite deformation of soft-EHL in the biological tissues can decrease the friction and failure which are in the relative moving surfaces of the tissues. The numerical calculation of classical EHL (hard-EHL) doesn’t consider enough for the factors of soft tissue features in the finite element method.
    In this paper, a complete soft-EHL linear-contact model is developed. In the model, the elastic half-space is replaced by the finite thickness analysis and considers geometric nonlinearity as well as finite strain theory. The surface velocities altered by the curvature effect are considered, and the load balance equation is formulated based on the deformed configuration. The film thickness, pressure distributions, and material deformation are analyzed under various entraining velocities, elastic modulus, and material thickness of the soft layer. Furthermore, the results can compare between soft-EHL and hard-EHL modeling assumptions. The analyses show that hard-EHL method is inappropriate on high load and low elastic modulus, and the soft-EHL model can be more accessible and reality.
    In the contact region, the hard EHL solver overestimates the pressure distribution and underestimates the film thickness and deformation affection. For the soft-EHL model, it can obtain smoother distribution of stress. Therefore, the soft-EHL model from this research can be a reference for the soft material design in the future.

    中文摘要 I Extended Abstract II 誌謝 XII 目錄 XIII 表目錄 XVI 圖目錄 XVII 符號總表 XX 第一章 緒論 1 1.1前言 1 1.2文獻回顧 1 1.2.1(硬)彈液動潤滑 ( Elastohydrodynamic lubrication, EHL) 2 1.2.2有限厚度彈液動潤滑 5 1.2.3軟彈液動潤滑(Soft-EHL) 7 1.2.4非等向性材料彈液動潤滑 9 1.3研究動機 11 1.4論文架構 12 第二章 彈液動潤滑理論 13 2.1簡介 13 2.2接觸幾何外形 13 2.3流體力學 15 2.3.1奈維爾-史托克方程式(Navier-Stokes Equation) 15 2.3.2雷諾方程式(Reynolds Equation) 17 2.4潤滑劑的黏度與密度 20 2.5本構方程式(Constitutive Equation) 22 2.6膜厚方程式 24 2.7負載平衡方程式 25 2.8摩擦力 26 第三章 數值分析 31 3.1有限元素分析 32 3.1.1Galerkin方法 32 3.1.2離散化形式 33 3.1.3Newton-Raphson迭代法 34 3.2網格獨立性分析 35 3.3模型驗證 37 第四章 軟彈液動潤滑模型 45 4.1軟彈液動模型建立 45 4.1.1軟彈液動潤滑-雷諾方程式 45 4.1.2軟彈液動潤滑-本構方程式 47 4.1.3軟彈液動潤滑-負載平衡方程 47 4.1.4軟彈液動潤滑-膜厚外形 48 4.1.5軟彈液動潤滑-數值計算 48 4.2結果與討論 49 4.3結論 56 第五章 橫向等向性材料之軟彈液動潤滑分析 67 5.1橫向等向性材料模型建立 67 5.2橫向等向性之軟彈液動潤滑-雷諾方程式 67 5.2.1橫向等向性之軟彈液動潤滑-本構方程式 68 5.2.2橫向等向性之軟彈液動潤滑-負載平衡方程 70 5.2.3軟彈液動潤滑-膜厚外形 70 5.3結果與討論 71 5.4結論 77 第六章 總論與未來展望 87 參考文獻 89 附錄一:雷諾方程式之物理意義 98

    [1] Tower, B., 1885, " Second Report on Friction Experiments (Experiments on the Oil Pressure in a Bearing)," Proc. Insi. Mech. Eng., pp. 58-70.
    [2] Petrov, N. P., 1883, "Friction in Machines and the Effect of the Lubricant," Inzh. Zh. St. Petersb. 4, pp. 535-564.
    [3] Reynolds, O., 1886, "On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil," Philos. Trans. R. Soc. London Ser. 177, pp. 157-234.
    [4] Martin, H. M., 1916, "Lubrication of Gear Teeth," Engineering (London), 102, pp. 119-121.
    [5] Peppler, W., 1936, "Untersuchungen uber die Druckubertragung bei Belasteten und Geschmierten Umlaufenden Achsparallelen Zylindern," Maschinenelemente-Tagung Aachen 1935, V.D.I., Berlin, 42.
    [6] Meldahl, A., 1941, "Contribution to the Theory of the Lubrication of Gears and of the Stressing of the Lubricated Flanks of Gear Teeth," Brown Boveri Rev., 28, pp. 374-382.
    [7] Gatcombe, E. K., 1945, "Lubrication Characteristics of Involute Spur Gears─A Theoretical Investigation," Trans. ASME, 67, pp. 177-185.
    [8] Blok, H., 1950, "Fundamental Mechanical Aspects of Thin Film Lubrication," Ann. N.Y. Acad. Sci., 53, pp. 779-804.
    [9] Grubin, A. N., 1949, "Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces," Book No. 30, Central Scientific Research Institute for Technology and Mechanical Engineering, Moscow (DSIR Translation), pp. 115-166.
    [10] Blok, H, 1965, "Elastohydrodynamic lubrication," communications. Proc. Instn Mech. Engrs, 180(3B), 237–238.
    [11] Cameron, A., 1985, "Righting 40 years-old wrong," Tribol. Int., 18(2), pp. 92.
    [12] Petrusevich, A. I., 1951, "Fundamental Conclusions from the Contact-Hydrodynamic Theory of Lubrication," Izv. Akad. Nauk SSR. Otd. Tekh. Nauk, 2, pp. 209-233.
    [13] Dowson, D., and Higginson, G. R., 1959, "A Numerical Solution to the Elastohydrodynamic Problem," J. Eng. Sci., 1, pp. 6-15.
    [14] Dowson, D., and Higginson, G. R., 1961, "New Roller Bearing Lubrication Formula," Engineering, 192, pp. 158-159.
    [15] Dowson, D., and Toyoda, S., 1979, "A Central Film Thickness Formula for Elastohydrodynamic Line Contacts," Proceedings of the Fifth Leeds-Lyon Symposium on Tribology, Mechanical Engineering Publications, Bury St. Edmunds, UK, pp. 60-65.
    [16] Dowson, D., and Higginson, G. R., 1966, "Elastohydrodynamic Lubrication," Pergamon, Oxford.
    [17] Ranger, A. P., Ettles, C. M. M., and Cameron, A., 1975, "The Solution of the Point Contact Elastohydrodynamic Problem," Proc. R. Soc. London, Ser. A, 346, pp. 227-244.
    [18] Hamrock, B. J., and Dowson, D., 1976, "Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part 1─Theoretical Formulation," ASME J. Lubr. Technol., 98, pp. 223-229.
    [19] Rohde, S. M., and Oh, K. P., 1975, "A Unified Treatment of Thick and Thin Film Elastohydrodynamic Problems by Using Higher Order Element Methods," Proc. R. Soc. London, Ser. A 343, pp. 315-331.
    [20] Oh, K. P., and Rohde, S. M., 1977, "Numerical Solution of the Point Contact Problem Using the Finite Element Method," Int. J. Numer. Methods Eng., 11, pp. 1507-1518.
    [21] Evans, H. P., and Snidle, R. W., 1981, "Inverse Solution of Reynolds Equation of Lubrication under Point Contact Elastohydrodynamic Conditions," ASME J. Lubr. Technol., 103, pp. 539-546.
    [22] Houpert, L. G., and Hamrock, B. J., 1986, "Fast Approach for Calculating Film Thicknesses and Pressures in Elastohydrodynamically Lubricated Contacts at Heavy Loads," ASME J. Tribol., 108, pp. 411-420.
    [23] Okamura, H., 1982, "A Contribution to the Numerical Analysis of Isothermal Elastohydrodynamic Lubrication," Proceedings of the Ninth Leeds-Lyon Symposium on Tribology, pp. 313-320.
    [24] Hertz., H., 1881, "On the contact of elastic solids," J. Reine Angew. Math., 92, pp. 156-171.
    [25] Meijers, P., 1968, "The Contact Problem of a Rigid Cylinder on an Elastic Layer," Appl. Sci. Res., 18, pp. 353-382.
    [26] Elsharkawy, A. A. and Hamrock, B. J., 1993, "A Numerical Solution for Dry Sliding Line Contact of Multilayered Elastic Bodies," J. Tribol., 115(2), pp. 237-246.
    [27] Elsharkawy, A. A. and Hamrock, B. J., 1994, "EHL of Coated Surfaces: Part I–Newtonian Results," J. Tribol. ASME, 116(1), pp. 29-36.
    [28] Barus, C., 1893, "Isothermals, Isopiestics, and Isometrics Relative to Viscosity," Am. J. Sci., Third Series, XLV, 266, pp. 87-96.
    [29] Thomas, B. W., Ham, W. R., and Dow, R. B., 1937, "Viscosity-Pressure Characteristics of Lubricating Oils," Indust. Eng. Chem., 31, pp. 1267-1270.
    [30] ASME Research Committee on Lubrication, 1953, "Viscosity and Density of Over 40 Lubricating Fluids of Known Composition at Pressure to 150,000 PSI and Temperature to 425F," ASME. New York.
    [31] Cameron, A., 1966, "The Principles of Lubrication," Wiley, New York.
    [32] Roelands, C. J. A., 1966, "Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils," Ph.D. thesis, Technische Hogeschool Delft, The Netherlands.
    [33] Zhu, D. and Wang, Q. J., 2011, "Elastohydrodynamic Lubrication: A Gateway to Interfacial Mechanics-Review and Prospect," J. Tribol. ASME, 133(4), pp. 041001-14.
    [34] Bennett, A. and Higginson, G. R., 1970, "Hydrodynamic Lubrication of Soft Solids," J. Mech. Eng. Sci., 12(3), pp. 218-222.
    [35] Conway, H. D., and Engel, P. A., 1973, "The Elastohydrodynamic Lubrication of a Thin Layer," Journal of Lubrication Technology, 95(3), 381-385.
    [36] Gupta, P. K., 1976, "On the Heavily Loaded Elastohydrodynamic Contacts of Layered Solids," Journal of Lubrication Technology, 98(3), 367-372.
    [37] Hooke, C. J., 1986, "The Elastohydrodynamic Lubrication of a Cylinder On an Elastic Layer," Wear, 111(1), pp. 83-99.
    [38] Jaffar, M. J., 1990, "Two-Dimensional Elastohydrodynamic Lubrication of Elastic Strips," Wear, 139, pp. 335-350.
    [39] Jaffar, M. J., 1991, "Pressure-Viscosity Effect on the Solutions of a Lubricated Thick Elastic Bonded Strip," Tribology International, 24(2), pp. 91-94.
    [40] Dowson, D., and Jin, Z., 1990, "Paper XI (i) The Influence of Elastic Deformation Upon Film Thickness in Lubricated Bearing with Low Elastic Modulus Coatings," Tribology Series, 17, pp. 263-269.
    [41] Jin, Z. M., 1988, "Micro–elastohydrodynamic Lubrication of Human Joints," Ph. D. thesis, University of Leeds.
    [42] Dowson, D. and Jin, Z. M., 1992, "Microelastohydrodynamic Lubrication of Low-elastic-modulus Solids on Rigid Substrates," J. Phys. D, 25, pp. A116-A123.
    [43] Jaffar, M. J., 2002, "On the Microelastohydrodynamic Lubrication of an Elastomeric Bonded Layer," Tribol. Int., 35, pp. 193-200.
    [44] Elsharkawy, A. A., Holmes, M. J. A., Evans, H. P. and Snidle, R. W., 2006, "Microelastohydrodynamic Lubrication of Coated Cylinders Using Coupled Differential Deflection Method," Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 220(J1), pp. 29-41.
    [45] Liu, Y. C., Chen, W. W., Zhu, D., Liu, S. and Wang, Q. J., 2007, "An Elastohydrodynamic Lubrication Model for Coated Surfaces in Point Contacts," ASME J. Tribol., 129, pp. 509-516.
    [46] Liu, Y. C., Zhu, D. and Wang, Q., 2008, "Effect of Stiff Coatings on EHL Film Thickness in Point Contacts," ASME J. Tribol., 130, 031501.
    [47] Wang, Z. J., Wang, W. Z., Wang, H. Z., Hu, Y. Z., 2009, "Stress Analysis on Layered Materials in Point Elastohydrodynamic Lubricated Contacts," Trib. Let., 35(3), pp. 229-244.
    [48] Dowson, D. and Wright, V., 1973, "Bio-tribology, in The Rheology of Lubricants," ed. T. C. Davenport, Applied Science Publishers, Barking, 1973, pp. 81-88.
    [49] McKee, C. T., Last, J. A., Russell, P., and Murphy, C. J., 2011, "Indentation Versus Tensile Measurements of Young’s Modulus for Soft Biological Tissues," Tissue Eng., Part B, 17(3), pp. 155-164.
    [50] Natali, A. N., Pavan, P. G., and Scarpa, C., 2004, "Numerical Analysis of Tooth Mobility: Formulation of a Non-Linear Constitutive Law for the Periodontal Ligament," Dent. Mater., 20(7), pp. 623-629.
    [51] Adams, M. J., Briscoe, B. J., and Johnson, S. A., 2007, "Friction and Lubrication of Human Skin," Tribol. Lett., 26(3), pp. 239-253.
    [52] Jones, M. B., Fulford, G. R., Please, C. P., McElwain, D. L. S., and Collins, M. J., 2008, "Elastohydrodynamics of the Eyelid Wiper, " Bull. Math. Biol., 70(2), pp. 323-343.
    [53] Hamrock, B. J., and Dowson, D., 1978, "Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus 1—Fully Flooded Conjunction," ASME J. Lubr. Technol., 100(2), pp. 236-245.
    [54] Dowson, D., and Jin, Z. M., 1986, "Micro-Elastohydrodynamic Lubrication of Synovial Joints," Eng. Med., 15(2), pp. 63-65.
    [55] Yao, J. Q., and Dowson, D., 1994, "Elastohydrodynamic Lubrication of Soft-Layered Solids at Elliptical Contacts—Part 1: Elasticity Analysis," Proc. Inst. Mech. Eng., Part J, 208(1), pp. 31-41.
    [56] Jin, Z. M., and Dowson, D., 2005, "Elastohydrodynamic Lubrication in Biological Systems," Proc. Inst. Mech. Eng., Part J, 219(5), pp. 367-380.
    [57] Chen, C. Y., Tseng, Y. F., Chu, L. M., and Li, W. L., 2013, "Soft EHL for Transversely Isotropic Materials," Tribol. Int., 67, pp. 240-253.
    [58] Moghani, T., Butler, J. P., and Loring, S. H., 2009, "Determinants of Friction in Soft Elastohydrodynamic Lubrication," J. Biomech., 42(8), pp. 1069-1074.
    [59] Stupkiewicz, S., 2009, "Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime," Computational Mechanics, 44(5), pp. 605-619.
    [60] Kudish, I. I., 2016, "Revision of a Fundamental Assumption in the Elastohydrodynamic Lubrication Theory and Friction in Heavily Loaded Line Contacts With Notable Sliding," ASME J. Tribol., 138(1), pp. 011501.
    [61] Stupkiewicz, S., Lengiewicz, J., Sadowski, P., and Kucharski, S., 2016, "Finite Deformation Effects in Soft Elastohydrodynamic Lubrication Problems," Tribol. Int., 93(Pt. B), pp. 511-522.
    [62] Willis, J. R., 1966, "Hertzian contact of anisotropic bodies," Journal of the Mechanics and Physics of Solids, 14(3), pp. 163-176.
    [63] Turner, J. R., 1980, "Contact on a transversely isotropic half-space, or between two transversely isotropic bodies," International Journal of Solids and Structures, 16(5), pp. 409-419.
    [64] Ovaert, T. C., 1993, "On the indentation of a transversely isotropic half-space with application to thin solid lubricant films," Trans. ASME, 1993, 115, pp. 650-657.
    [65] Lovell, M., 1998, "Analysis of contact between transversely isotropic coated surfaces: development of stress and displacement relationships using FEM," Wear, 214(2), pp. 165-174.
    [66] Ning, X., Lovell, M., and Slaughter, W. S., 2006, "Asymptotic solutions for axisymmetric contact of a thin, transversely isotropic elastic layer," Wear, 260(7-8), pp. 693-698.
    [67] Swanson, S. R., 2005, "Contact deformation and stress in orthotropic plates. Composites Part A: Applied Science and Manufacturing," 36(10), pp. 1421-1429.
    [68] Majeed, M. A., Yigit, A. S., and Christoforou, A. P., 2012, "Elastoplastic contact/impact of rigidly supported composites," Composites Part B: Engineering, 43(3), pp.1244-1251.
    [69] Chu, L. M., Chen, C. Y., Tee, C. K., Chen, Q. D., and Li, W. L., 2013, "Elastohydrodynamic Lubrication Analysis for Transversely Isotropic Coating Layer," ASME J. Tribol., 136(3), pp. 031502.
    [70] Wang, Z., Zhu, D., and Wang, Q., 2014, "Elastohydrodynamic lubrication of inhomogeneous materials using the equivalent inclusion method," Journal of Tribology, 136(2).
    [71] Wang, Z., and Zhang, Y., 2019, "An Efficient Numerical Model of Elastohydrodynamic Lubrication for Transversely Isotropic Materials," Journal of Tribology, 141(9).
    [72] Navier, C. L. M. H., 1823, "Memoire sur les lois du mouvement des fruides," Mem. Acad. Sci. Inst. Fr., 6, pp. 389-416.
    [73] Stokes, G. G., 1845, "On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids," Trans. Cambridge Philos. Soc., 8. pp. 287-341.
    [74] Dowson, D. and Higginson, G.R., 1966, "Elasto-hydrodynamic Lubrication; The Fundamentals of Roller and Gear Lubrication," Pergamon Press, Oxford, pp. 1-235.
    [75] Li, L., and Hao, C. T., 2011, "Constraints on anisotropic parameters in transversely isotropic media and the extensions to orthorhombic media," Chinese Journal of Geophysics, 54(6), pp. 798-809.
    [76] Hamrock, B. J., Schmid, S. R., and Jacobson, B. O., 2004, "Fundamentals of Fluid Film Lubrication," 2nd ed., Marcel Dekker, New York, Chap. 7, Sec. 3.

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