臺灣博碩士論文加值系統

本文提出一種新的橢圓溝槽設計，以改善傳統含人字形溝槽頸軸承的性能。文中的第一部分，先以寬頻元素法為基礎，發展可求解含人字形溝槽頸軸承的壓力分佈與動態係數的數值程式。程式中考慮了溝槽與溝岸交接的界面，以質量守恆處理液膜不連續的問題。此外，程式擁有可處理溝槽為曲線形狀的彈性。結果顯示，程式解出的負載，比其他文獻的數值結果更準確。當空蝕現象發生時，採用溝槽不連續的質量守恆搭配Elrod算則處理空蝕現象，可以進一步改善在高偏心比之負載的準確度。
本文的第二部分。提出含橢圓溝槽之新形狀的軸承。並使用上述發展的數值程式，分析其性能。橢圓溝槽軸承的負載、穩定性、洩漏量與傳統人字形溝槽軸承比較，結果顯示，本文提出的橢圓形溝槽擁有高徑向力、高負載、和低洩漏量。接著，本文找出軸承運轉時，最佳化溝槽參數，使軸承有最大的徑向力。最後，本文比較人字形、四邊溝槽、八邊溝槽、及橢圓形溝槽軸承表面的負載分布。以說明橢圓形溝槽的設計，如何增加負載。橢圓形溝槽軸承在軸向的負載分布，較人字形溝槽軸承均勻。在軸承中央處較人字形溝槽低的負載，會被軸承兩端較高的負載抵銷，於是達到較人字形溝槽高的負載。
本文的最後一部分，將橢圓形溝槽應用於可反轉的軸承上，以改善可反轉人字形溝槽的負載，並以數值方法探討性能改善的程度。橢圓溝槽可反轉軸承的負載、穩定性、耗能與傳統人字形溝槽可反轉軸承比較。比較結果顯示，橢圓形溝槽可反轉軸承的負載較高，耗能較低。橢圓溝槽可反轉軸承的高壓區不只在正轉的壓力產生區，也在反轉需要的壓力恢復區產生。此外，比較人字形、及橢圓形溝槽可反轉軸承表面的負載分布。以說明橢圓形溝槽的設計，如何增加負載。最後，在徑向剛性係數為考量的最佳化參數之下，橢圓形溝槽可反轉軸承的穩定性比人字形溝槽可反轉軸承優異。

A novel elliptical groove is proposed in this work to improve the performance of conventional journal bearings. Firstly, the present work utilizes the spectral element method to calculate the pressure distribution and dynamic coefficients of herringbone-grooved journal bearings (HGJBs), in which the thickness of the fluid film changes abruptly in the groove-ridge region. Conservation of mass is adopted to solve the problem. Additionally, the present method can be adopted for grooves with curvy geometry. It shows that for the case of HGJB, the numerical result by the present method is more accurate than the numerical results found in the literature. Furthermore, employing the present method with the Elrod’s algorithm can improve the accuracy of deriving loads of HGJBs when cavitation occurs.
In the secondary part of this work, the novel elliptical grooves are proposed. This work utilizes novel elliptical grooves on a journal bearing and analyzes the characteristics of the elliptical-grooved journal bearings (EGJB) numerically. Load capacity, stability parameter, and total side leakage of the EGJB are compared with those of the HGJB. The comparison shows that the introduced EGJB have higher radial force, higher load capacity, and lower side leakage than the conventional HGJB. The optimum geometrical parameters of groove of EGJB are investigated based on the maximum radial force. Finally, the load distributions of several grooved journal bearings are compared to elucidate how elliptical grooves enhance load characteristics. The load distribution along the axial direction in EGJB is more uniform than that in the HGJB. The low load near the bearing center for the EGJB may be offset by the load away the bearing center; thus, a higher total load capacity than that of HGJB is achieved.
In the end of this work, to improve the performance of the reversible rotation grooved journal bearing (Rev-HGJB), this work utilizes elliptical grooves on a reversible rotation journal bearing (Rev-EGJB) and analyzes its characteristics numerically. Load capacity, pressure distribution, power loss, and dimensionless radial stiffness of the Rev-EGJB are compared with those of the Rev-HGJB. The comparison shows that the introduced Rev-EGJB exhibits higher load capacity and lower power loss than the Rev-HGJB. A larger high pressure region in the Rev-EGJB than that in the Rev-HGJB is achieved not only in the pressure-generated region, but also in the pressure-restored region. Furthermore, the load distributions of the Rev-HGJB and Rev-EGJB are compared to elucidate how elliptical grooves enhance load characteristics. Ultimately, the radial stiffness of the Rev-EGJB compared with that of the Rev-HGJB with the optimum geometry is also shown to be greater; thus, the Rev-EGJB is more stable than the Rev-HGJB.

摘要 i
Abstract iii
Contents vii
List of Figures x
List of Tables xv
Nomenclature xvi
1. Introduction 1
1-1 Current Applications of Grooved Journal Bearings 1
1-2 Research Needs for Groove Appearances 4
1-3 Stability Criteria 5
1-4 Cavitation Model 6
1-5 Analysis Methods 7
1-5-1 Discretization Method 7
1-5-2 Treatment at the Discontinuity of Groove-Ridge Region 9
1-6 Dissertation Outline 11
2. Governing Equations 13
2-1 Reynolds Equation 13
2-2 Elrod’s Cavitation Algorithm 18
2-3 Stability Parameter 19
2-4 Groove Profile 20
3. Numerical Method 23
3-1 Spatial Discretization- Spectral Element Method (SEM) 23
3-2 Treatment in Groove-Ridge Discontinuity 30
3-2-1 For 1-D Step-Slider Bearing 30
3-2-2 For 2-D HGJB with Reynolds Equation 33
3-2-3 For 2-D HGJB with Elrod’s Algorithm 36
3-3 Grid Independent Test 37
3-3-1 HGJB 37
3-3-2 EGJB 40
4. Validation 45
4-1 Load Capacity 45
4-1-1 One-dimensional Step-Slider Bearing 45
4-1-2 Load Comparison of HGJB 47
4-1-3 Load Comparison of HGJB with Elrod’s Model 49
4-1-4 Validation of EGJB 53
4-2 Validation of Critical Mass 56
5. Effect of HGJB’s Appearance on Stability 61
5-1 Effect of Change in Groove Angle on Critical mass 61
5-2 Effect of Change in Groove Depth on Critical mass 65
5-3 Effect of Change in Groove Width on Critical Mass 66
5-4 Efficiency of the Present Method on Critical Mass 67
6. Performance Enhancement Using Elliptical Grooves 69
6-1 Performance of EGJB 69
6-1-1 Effect on Load Capacity 69
6-1-2 Effect on Stability 71
6-1-3 Effect on Side Leakage 73
6-1-4 Effect on Reducing Cavitation 75
6-2 Optimum Groove Parameters for Stability 78
6-3 Comparison of the Load Distribution 84
7. Performance Enhancement on Rev-EGJB 89
7-1 Groove Profile 89
7-2 Validation 91
7-3 Comparison of the Rev-EGJB and the Rev-HGJB 94
7-3-1 Rev-EGJB Mesh 95
7-3-2 Comparison of the Load Capacities 96
7-3-3 Comparison of the Pressure Distributions in the Fluid Film 99
7-4 Comparison of Power Losses 102
7-5 The Effect of Groove’s Appearance on Radial Stiffness 103
7-6 The Optimum Parameters of Rev-EGJB for Stability 108
8. Conclusions 111
9. Future Work 113
References A1
Appendix A Evaluation of Dimensionless Critical Mass A5

1.Asada T, Saito H, Asaida Y, Itoh K. Design of hydrodynamic bearings for high-speed hdd. Microsystem Technologies 2002; 8(2-3): 220-226.
2.Liu CS, Lin PD, Tsai MC. A miniature spindle motor with fluid dynamic bearings for portable storage device applications. Microsystem Technologies 2009; 15(7): 1001-1007.
3.Ohmi T. Non-repeatable runout of ball-bearing spindle-motor for 2.5 double prime hdd. IEEE Transactions on Magnetics 1996; 32(3-2): 1715-1720.
4.Chao PCP, Huang JS. Calculating rotordynamic coefficients of a ferrofluid-lubricated and herringbone-grooved journal bearing via finite difference analysis. Tribology Letters 2005; 19(2): 99-109.
5.Muijderman EA. Grease-lubricated spiral groove bearings. Tribology international 1979; 12: 131-137.
6.Kawabata N, Ozawa Y, Kamaya S, Miyake Y. Static characteristics of the regular and reversible rotation type herringbone grooved journal bearing. Journal of Tribology, Transactions of the ASME 1989; 111(3): 484-490.
7.Zhang QD, Winoto SH, Chen SX, Yang JP. A bi-directional rotating fluid bearing system. Microsystem Technologies 2002; 8(2002): 271-277.
8.Junmei W, Jiankang W, Lee TS, Shu C. A numerical study of cavitation foot-prints in liquid-lubricated asymmetrical herringbone grooved journal bearings. International Journal of Numerical Methods for Heat and Fluid Flow 2002; 12(5): 518-540.
9.Leuthold H, Jennings DJ, Nagarathnam L, Grantz A, Parsoneault S. Sinusoidal grooving pattern for grooved journal bearing. 1999: U. S. Patent 5,908,247.
10.Liu CS, Tsai MC, Yen RH, Lin PD, Chen CY. Analysis and validations of a novel hydrodynamic grooved journal bearing. Journal of Chinese Society of Mechanical Engineers: (summitted, in revise).
11.Kang K, Rhim Y, Sung K. A study of the oil-lubricated herringbone-grooved journal bearing-part 1: Numerical analysis. Journal of Tribology, Transactions of the ASME 1996; 118(4): 906-911.
12.Gad AM, Nemat-Alla MM, Khalil AA, Nasr AM. On the optimum groove geometry for herringbone grooved journal bearings. Journal of Tribology,Transactions of the ASME 2006; 128(3): 585-593.
13.Kirk RG, Gunter EJ. Stability and transient motion of a plain journal mounted in flexible damped supports. Journal of Engineering for Industry-Transactions of the ASME 1976; 98(2): 576-592.
14.Lund JW. Review of the concept of dynamic coefficients for fluid film journal bearings. Journal of Tribology, Transactions of the ASME 1987; 109(1): 37-41.
15.Bonneau D, Absi J. Analysis of aerodynamic journal bearings with small number of herringbone grooves by finite element method. Journal of Tribology, Transactions of the ASME 1994; 116(4): 698-704.
16.Zirkelback N, San Andrés L. Finite element analysis of herringbone groove journal bearings: A parametric study. Journal of Tribology, Transactions of the ASME 1998; 120(2): 234-240.
17.Rao TVVLN, Sawicki JT. Stability characteristics of herringbone grooved journal bearings incorporating cavitation effects. Journal of Tribology, Transactions of the ASME 2004; 126(2): 281-287.
18.Jakobsson B, Floberg L. The finite journal bearing considering vaporization. Charmers Tekniska Hoegskolas Handlingar 1957; 190: 1-116.
19.Lee TS, Liu YG, Winoto SH. Analysis of liquid-lubricated herringbone grooved journal bearings. International Journal of Numerical Methods for Heat and Fluid Flow 2004; 14(3): 341-365.
20.Jang GH, Chang DI. Analysis of a hydrodynamic herringbone grooved journal bearing considering cavitation. Journal of Tribology, Transactions of the ASME 2000; 122(1): 103-109.
21.Patera AT. A spectral element method for fluid dynamics: Laminar flow in a channel expansion. Journal of Computational Physics 1984; 54: 468-488.
22.Korczak KZ, Patera AT. An isoparametric spectral element method for solution of the navier-stokes equations in complex geometry. Journal of Computational Physics 1986; 62: 361-382.
23.Schneidesch CR, Deville MO. Chebyshev collocation method and multi-domain decomposition for navier-stokes equations in complex curved geometries. Journal of Computational Physics 1993; 106: 234-257.
24.Gordon WJ, Hal CA. Transfinite element methods: Blending-function interpolation over arbitrary curved element domains. Numerische Mathematik 1973; 21(2): 109-129.
25.Karniadakis GE. Spectral element simulations of laminar and turbulent flows in complex geometries. Applied Numerical Mathematics 1989; 6: 85-105.
26.Gerritsma M, van der Bas R, De Maerschalck B, Koren B, Deconinck H. Least-squares spectral element method applied to the euler equations. International Journal for Numerical Methods in Fluids 2008; 57(9): 1371-1395.
27.Stiller J, Fladrich U. Factorization techniques for nodal spectral elements in curved domains. SIAM Journal on Scientific Computing 2008; 30(5): 2286-2301.
28.Kopriva DA. Metric identities and the discontinuous spectral element method on curvilinear meshes. Journal of Scientific Computing 2006; 26(3): 301-327.
29.Vohr JH, Chow CY. Characteristics of herringbone grooved gas lubricated journal bearings. Journal of Basic Engineering 1965; 87: 568-578.
30.Faria MTC. Some performance characteristics of high speed gas lubricated herringbone groove journal bearings. JSME International Journal, Series C 2001; 44(3): 775-781.
31.Arghir M, Alsayed A, Nicolas D. The finite volume solution of the reynolds equation of lubrication with film discontinuities. International Journal of Mechanical Sciences 2002; 44(10): 2119-2132.
32.Hernandez P, Boudet R. Modelling of the behavior of dynamical gas seals: Calculation with a finite element method implicitly assuring the continuity of flow. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 1995; 209(3): 195-201.
33.Hirayama T, Sakurai T, Yabe H. A theoretical analysis considering cavitation occurrence in oil-lubricated spiral-grooved journal bearings with experimental verification. Journal of Tribology, Transactions of the ASME 2004; 126(3): 490-498.
34.Elrod HG. A cavitation algorithm. ASME Journal of Lubrication Technology 1981; 103: 350-354.
35.Hamrock BJ, Fundamentals of fluid film lubrication. McGraw-Hill, 1994.
36.Yen RH, Chen CY. Enhancement of journal bearings characteristics using a novel elliptical grooves. Proceedings of the Institution of Mechanical Engineers, Part J Journal of Engineering Tribology 2009: in press.
37.Hirs GG. The load capacity and stability characteristics of hydrodynamic grooved journal bearings. ASLE Transactions 1965; 8: 296-305.
38.Chen CY, Yen RH, Chang CC. Spectral element analysis of herringbone grooved journal bearings with groove-ridge discontinuity. International Journal for Numerical Methods in Fluids 2010: in press.
39.Wang JK, Khonsari MM. Effects of oil inlet pressure and inlet position of axially grooved infinitely long journal bearings. Part i: Analytical solutions and static performance. Tribology international 2008; 41: 119-131.