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研究生: 王鉅棟
Wang, Chu-Tung
論文名稱: 具黏彈性襯套之頸軸承液動潤滑分析
Hydrodynamic Lubrication Analysis of a Journal Bearing with a Viscoelastic Bushing
指導教授: 李旺龍
Li, Wang-Long
學位類別: 碩士
Master
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: 2026
畢業學年度: 114
語文別: 中文
論文頁數: 143
中文關鍵詞: 黏彈性暫態分析高分子襯套Kelvin-Voigt 模型
外文關鍵詞: viscoelasticity, transient analysis, Kelvin–Voigt model, polymer bushing
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  • 在傳統頸軸承液動潤滑分析中,過往多以穩態分析為主,且常假設與油膜接觸之軸承襯套為剛性或線彈性材料。然而,近年來因經濟效益、耐磨耗性、減震能力,以及降低異物碎屑造成軸頸損傷等考量,高分子材料逐漸被應用於軸承襯套設計中。早期高分子襯套多應用於水潤滑軸頸軸承,主要利用其良好的耐磨耗性、耐腐蝕性與低摩擦特性,改善傳統金屬襯套在水潤滑環境下可能面臨之磨損與潤滑不足問題。隨著材料技術與加工製程逐漸成熟,近年來高分子襯套之機械強度、耐溫性與尺寸穩定性已有明顯提升,使其應用範圍不再侷限於水潤滑軸頸軸承,亦逐漸具備應用於礦物油等油體潤滑環境之可行性。
    本研究採用雷諾方程式描述油膜壓力分佈,並將襯套變形量納入膜厚方程式中;其中黏彈性襯套以 Kelvin-Voigt模型表示,藉由彈性項與黏滯項描述襯套材料之變形與延遲反應。在給定負載與轉速條件下,分別分析剛性襯套、線彈性襯套及不同黏滯係數之黏彈性襯套,並比較其油膜壓力、膜厚分佈、變形量、應變率、摩擦力、軸心軌跡與平衡位置。
    結果表明襯套變形會改變油膜厚度與壓力分佈,進而影響軸心平衡位置與暫態軌跡;而黏滯係數則主要影響轉子由暫態進入穩態之速度與變形延遲程度。當黏滯係數較高時,襯套變形反應較慢,初期行為較接近剛性襯套;但在一段時間運轉後,轉子軌跡仍會逐漸趨於穩定。因此,相較於傳統線彈性模型,考慮黏彈性襯套效應更能反映高分子襯套在實際運轉下之時間延遲變形與阻尼特性;同時在高黏滯係數條件下,襯套可於暫態初期呈現較接近剛性襯套之穩定承載行為,並兼具高分子材料之耐磨耗、減震與降低軸頸損傷等優點。本研究可作為後續高分子襯套軸承設計與暫態性能分析之參考。

    Traditional hydrodynamic lubrication analyses of journal bearings are mostly based on steady-state conditions, and the bearing bushing is often assumed to be rigid or linearly elastic. In recent years, polymer materials have been increasingly used in bearing bushings because of their advantages in cost, wear resistance, vibration reduction, and reduced journal damage. Although polymer bushings were mainly applied to water-lubricated systems in the past, improvements in material properties have made their use in oil-lubricated systems, such as mineral oil environments, more feasible.

    In this study, the Reynolds equation is used to describe the oil film pressure distribution, and bushing deformation is included in the film thickness equation. The viscoelastic behavior of the bushing is modeled using the Kelvin–Voigt model. Rigid, linearly elastic, and viscoelastic bushings with different viscosity coefficients are compared under given load and rotational speed conditions.

    The results show that bushing deformation affects the oil film thickness, pressure distribution, journal center trajectory, and equilibrium position. The viscosity coefficient mainly influences the deformation delay and transient convergence behavior. Compared with the linearly elastic model, the viscoelastic model can better describe the time-dependent deformation and damping characteristics of polymer bushings. This study can serve as a reference for the design and dynamic analysis of polymer bushing bearings.

    中文摘要 I Extended Abstract II 誌謝 XVIII 目錄 XIX 表目錄 XXI 圖目錄 XXI 符號表 XXIV 第一章 緒論 1 1.1前言 1 1.2文獻回顧 2 1.2.1潤滑軸承發展 2 1.2.2暫態潤滑理論與暫態軌跡模擬 4 1.2.3彈性變形量 5 1.2.4黏彈性變形量 6 1.3研究動機與目的 9 1.4本文內容架構 10 第二章 研究理論 12 2.1 雷諾方程式(Reynolds方程式) 12 2.1.1 質量守恆方程式 13 2.1.2 動量守恆方程式 14 2.1.3Navier-Stokes方程式 16 2.1.4 雷諾方程式 17 2.2 油膜厚度方程式 21 2.3 軸承負載方程式 23 2.4 摩擦扭矩與摩擦係數 24 2.5 線彈性力學 25 2.6 黏彈性力學 28 2.7 空蝕效應 31 第三章 數值方法 35 3.1 有限元素法 35 3.1.1 空間離散化 36 3.1.2 伽遼金法 36 3.1.3 牛頓 拉佛森法 37 3.2 模型計算流程和網格靈敏度測試 38 3.3 模型驗證 39 3.3.1 暫態轉子軌跡圖之模型驗證 39 第四章 模擬結果與討論 46 4.1 襯套材料選用與操作條件 46 4.1.1 線彈性襯套 47 4.1.2 黏彈性襯套 47 4.2不同黏滯係數下之軸承性能分析 50 4.2.1 黏滯係數對轉子軌跡的影響 51 4.2.2 黏滯係數對黏彈軸承襯套變形量的影響 52 4.2.3 黏滯係數對軸承承載的影響 54 4.2.4 黏滯係數對應變率、變形速度的影響 55 4.2.5 黏滯係數對軸承摩擦力矩與摩擦係數的影響 55 4.3楊氏模數與延遲時間對黏彈性軸承性能影響 56 4.3.1楊氏模數於固定延遲時間條件下軸承軌跡的影響 57 4.3.2 楊氏模數於固定延遲時間條件下黏彈襯套變形量的影響 57 4.3.3楊氏模數於固定黏滯係數條件下轉子軌跡的影響 58 4.3.4楊氏模數於固定黏滯係數條件下黏彈襯套變形量的影響 58 4.4轉子質量對軸承性能的影響 59 4.4.1轉子質量對轉子軌跡的影響 60 4.4.2轉子質量對軸承襯套變形量的影響 61 4.4.3轉子轉速對軸承襯套的影響 62 4.5軸承間隙對軸承性能的影響 63 4.5.1軸承間隙對轉子軌跡的影響 63 4.5.2軸承間隙對轉子平衡時間的影響 65 第五章 結論 105 參考文獻 107 附錄一 113

    [1] Hirn, G.-A., 1858, “Sur les Principaux Phénomènes que Présentent les Frottements Médiats, et sur les Diverses Manières de Déterminer la Valeur Mécanique des Matières Employées au Graissage des Machines,” Bulletin de la Société Industrielle de Mulhouse, 26, pp. 188–237.
    [2] Petrov, N. P., 1883, “Friction in Machines and the Effect of the Lubricant,” Inzhenernyi Zhurnal, St. Petersburg, Russia.
    [3] Tower, B., 1884, “First Report on Friction Experiments,” Proceedings of the Institution of Mechanical Engineers, 35(1), pp. 29–35.
    [4] 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,” Philosophical Transactions of the Royal Society of London, 177, pp. 157–234.
    [5] Martin, H. M., 1916, “Lubrication of Gear Teeth,” Engineering, 102, p. 119.
    [6] Dowson, D., and Taylor, C. M., 1979, “Cavitation in Bearings,” Annual Review of Fluid Mechanics, 11(1), pp. 35–65.
    [7] Sinhasan, R., and Chandrawat, H. N., 1988, “An Elastohydrodynamic Study on Two-Axial-Groove Journal Bearings,” Tribology International, 21(6), pp. 341–348.
    [8] Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M., 1997, Hydrodynamic Lubrication: Bearings and Thrust Bearings, Elsevier, Amsterdam, The Netherlands.
    [9] Wang, N., and Chang, C., 1999, “An Application of Newton’s Method to the Lubrication Analysis of Air-Lubricated Bearings,” Tribology Transactions, 42(2), pp. 419–424.
    [10] Nicoletti, R., and Santos, I. F., 2003, “Linear and Non-Linear Control Techniques Applied to Actively Lubricated Journal Bearings,” Journal of Sound and Vibration, 260(5), pp. 927–947.
    [11] Gertzos, K. P., Nikolakopoulos, P. G., and Papadopoulos, C. A., 2008, “CFD Analysis of Journal Bearing Hydrodynamic Lubrication by Bingham Lubricant,” Tribology International, 41(12), pp. 1190–1204.
    [12] Booker, J. F., 1965, “Dynamically Loaded Journal Bearings: Mobility Method of Solution,” Journal of Basic Engineering, 87, pp. 537–546.
    [13] Kirk, R. G., and Gunter, E. J., Jr., 1970, Transient Journal Bearing Analysis, NASA Contractor Report NASA CR-1549, National Aeronautics and Space Administration, Washington, DC.
    [14] Jain, S. C., and Sinhasan, R., 1983, “Performance of Flexible Shell Journal Bearings With Variable Viscosity Lubricants,” Tribology International, 16(6), pp. 331–338.
    [15] Jain, S. C., Sinhasan, R., and Pilli, S. C., 1990, “Transient Response of a Journal Supported on Elastic Bearings,” Tribology International, 23(3), pp. 201–209.
    [16] Li, W. L., Chu, H. M., and Chen, M. D., 2006, “The Partially Wetted Bearing—Extended Reynolds Equation,” Tribology International, 39, pp. 1428–1435.
    [17] Bollada, P. C., and Phillips, T. N., 2007, “On the Effects of a Compressible Viscous Lubricant on the Load-Bearing Capacity of a Journal Bearing,” International Journal for Numerical Methods in Fluids, 55(12), pp. 1091–1120.
    [18] Chen, C. Y., Chen, C. D., and Li, W. L., 2013, “Characteristics of Journal Bearings With Anisotropic Slip,” Tribology International, 61, pp. 144–155.
    [19] Li, W. L., Huang, Z. H., Lin, C. S., Chen, T. H., and Shyu, S. H., 2019, “On the Linear Stability Analysis of Journal Bearings—Consideration of Coupled Effects of Anisotropic Slip and Surface Roughness,” Tribology International, 137, pp. 254–266.
    [20] Zhu, J., Wei, G., Peng, Z., Xia, Z., Zheng, L., and Zhu, H., 2022, “Analysis of Underwater Explosion Shock on Ship Shaft Stern Bearing Lubrication Characteristics Under Different Bearing Working Conditions,” International Journal of Naval Architecture and Ocean Engineering, 14, Art. No. 100444.
    [21] Chaudhary, S., and Verma, R., 2025, “A Comprehensive Review of Journal Bearing Models: Comparative Analysis of Thermal, Elastic, and Hydrodynamic Approaches Considering Misalignment, Surface Texture, Turbulence, and Cavitation,” Journal of Tribology, 147(11), Art. No. 110802.
    [22] Dyson, A., 1976, “The Failure of Elastohydrodynamic Lubrication of Circumferentially Ground Discs,” Proceedings of the Institution of Mechanical Engineers, 190(1), pp. 699–711
    [23] Shi, F., and Wang, Q. J., 1998, “A Mixed-TEHD Model for Journal-Bearing Conformal Contacts—Part I: Model Formulation and Approximation of Heat Transfer Considering Asperity Contact,” Journal of Tribology, 120(2), pp. 198–205.
    [24] Mokhiamer, U. M., Crosby, W. A., and El-Gamal, H. A., 1999, “A Study of a Journal Bearing Lubricated by Fluids With Couple Stress Considering the Elasticity of the Liner,” Wear, 224(2), pp. 194–201.
    [25] Ebrat, O., Mourelatos, Z. P., Vlahopoulos, N., and Vaidyanathan, K., 2004, “Calculation of Journal Bearing Dynamic Characteristics Including Journal Misalignment and Bearing Structural Deformation,” Tribology Transactions, 47(1), pp. 94–102.
    [26] Osman, T. A., 2004, “Effect of Lubricant Non-Newtonian Behavior and Elastic Deformation on the Dynamic Performance of Finite Journal Plastic Bearings,” Tribology Letters, 17(1), pp. 31–40.
    [27] Meng, F., and Chen, Y., 2015, “Analysis of Elasto-Hydrodynamic Lubrication of Journal Bearing Based on Different Numerical Methods,” Industrial Lubrication and Tribology, 67(5), pp. 486–497.
    [28] Chun, S. M., and Khonsari, M. M., 2016, “Wear Simulation for Journal Bearings Operating Under Aligned Shaft and Steady Load During Start-Up and Coast-Down Conditions,” Tribology International, 97, pp. 440–466.
    [29] Cubillo, A., Uriondo, A., and Perinpanayagam, S., 2017, “Computational Mixed TEHL Model and Stribeck Curve of a Journal Bearing,” Tribology Transactions, 60(6), pp. 1053–1062.
    [30] Hong, S. H., 2018, “A New Clearance Design Method for Reciprocating Fuel Pumps of Medium-Speed Diesel Engines,” Tribology Transactions, 61(4), pp. 773–783.
    [31] Jadhav, S., Thakre, G., and Sharma, S. C., 2018, “Numerical Modeling of Elastohydrodynamic Lubrication of Line Contact Lubricated With Micropolar Fluid,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(6), Art. No. 326.
    [32] Gong, J., Jin, Y., Liu, Z., Jiang, H., and Xiao, M., 2019, “Study on Influencing Factors of Lubrication Performance of Water-Lubricated Micro-Groove Bearing,” Tribology International, 129, pp. 390–397.
    [33] 施震陽,2019,「含非等向性滑移與彈性變形之頸軸承液動分析」,碩士論文,國立成功大學材料科學及工程學系,台南市。
    [34] 許祐瑜,2021,「含非等向性滑移與彈性變形效應之頸軸承線性穩定分析」,碩士論文,國立成功大學材料科學及工程學系,台南市
    [35] 徐銘楷,2023,「利用機器學習做含彈性變形量之頸軸承液動分析」,碩士論文,國立成功大學綠色應用材料研究所,台南市。
    [36] Maxwell, J. C., 1867, “On the Dynamical Theory of Gases,” Philosophical Transactions of the Royal Society of London, 157, pp. 49–88.
    [37] Boltzmann, L., 1874, “Zur Theorie der Elastischen Nachwirkung,” Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, Wien, Mathematisch-Naturwissenschaftliche Classe, 70, pp. 275–306.
    [38] Voigt, W., 1892, “Ueber die Innere Reibung Fester Körper, Insbesondere der Metalle,” Annalen der Physik, 283, pp. 671–693.
    [39] Volterra, V., 1909, “Sulle Equazioni Integro-Differenziali della Teoria dell’Elasticità,” Rendiconti della Reale Accademia dei Lincei, 19, pp. 333–339.
    [40] Burgers, J. M., 1935, “Mechanical Considerations Model Systems Phenomenological Theories of Relaxation and of Viscosity,” in First Report on Viscosity and Plasticity, North-Holland Publishing Company, Amsterdam, The Netherlands.
    [41] Flügge, W., 1975, Viscoelasticity, 2nd ed., Springer-Verlag, Berlin, Germany.
    [42] Roberts, G. W., and Walters, K., 1992, “On Viscoelastic Effects in Journal-Bearing Lubrication,” Rheologica Acta, 31(1), pp. 55–62.
    [43] Berker, A., Bouldin, M. G., Kleis, S. J., and VanArsdale, W. E., 1995, “Effect of Polymer on Flow in Journal Bearings,” Journal of Non-Newtonian Fluid Mechanics, 56, pp. 333–347.
    [44] Holzapfel, G. A., 1996, “On Large Strain Viscoelasticity: Continuum Formulation and Finite Element Applications to Elastomeric Materials,” International Journal for Numerical Methods in Engineering, 39(22), pp. 3903–3926.
    [45] Phillips, T. N., Need, A., Davies, A. R., Williamson, J. R., and Scales, L. E., 1998, “The Effect of Viscoelasticity on the Performance of Dynamically Loaded Journal Bearings,” SAE Technical Paper No. 982639, SAE Transactions.
    [46] Miszczak, A., 2004, “Viscoelastic Unsteady Lubrication of Radial Slide Journal Bearing at Impulsive Motion,” Industrial Lubrication and Tribology, 56(1), pp. 9–21.
    [47] 楊挺青、羅文波、徐平、龐銀濤、剛芊榮,2004,《黏彈性理論與應用》,科學出版社,北京。
    [48] Bavastri, C. A., Ferreira, E. M. S., de Espíndola, J. J., and Lopes, E. M. O., 2008, “Modeling of Dynamic Rotors With Flexible Bearings Due to the Use of Viscoelastic Materials,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, 30(1), pp. 22–29.
    [49] Wang, Y. Q., and Sun, W. L., 2012, “Experimental Study on the Lubrication Behaviors of Seawater-Lubricated Thordon Bearings,” Key Engineering Materials, 500, pp. 297–300.
    [50] Wang, Y. Q., and Zhang, L. J., 2012, “Characteristics and Outline of Water-Lubricated Thordon Bearing,” Advanced Materials Research, 496, pp. 355–358.
    [51] Kwacz, M., and Rymuza, Z., 2010, “Frictional Behavior of Miniature Journal Polymer-on-Polymer Bearings,” in Polymer Tribology, M. R. Chowdhury, ed., World Scientific, Singapore, Chap. 8, pp. 267–311.
    [52] Miyanaga, N., and Tomioka, J., 2016, “Effect of Support Stiffness and Damping on Stability Characteristics of Herringbone-Grooved Aerodynamic Journal Bearings Mounted on Viscoelastic Supports,” Tribology International.
    [53] Wang, H., Liu, Z., Zou, L., and Yang, J., 2017, “Influence of Both Friction and Wear on the Vibration of Marine Water-Lubricated Rubber Bearing,” Wear, 376–377, pp. 920–930.
    [54] Ribeiro, E. A., Alves, D. S., Cavalca, K. L., and Bavastri, C. A., 2021, “Stability Analysis and Optimization of a Hybrid Rotating Machinery Support Combining Journal Bearings With Viscoelastic Supports,” Mechanism and Machine Theory, 156, Art. No. 104166.
    [55] Küçükoğlu Doğan, B., and Karaçay, T., 2023, “Investigation of Polymer Hybrid Ball Bearings’ Dynamic Behaviour,” Muş Alparslan Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 4(2), pp. 40–49.
    [56] Xiang, G., Wang, L., Fillon, M., Zhou, C., and Yang, T., 2026, “Coupled Nonlinear Dynamics and Mixed Thermal-Visco-Hyperelastic Hydrodynamic Lubrication in Water-Lubricated Rubber Bearings,” Tribology International, 214, Art. No. 111246.

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