微载荷含油轴承摩擦学性能研究
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摘要
信息技术和微型机电设备中，含油轴承的应用日益广泛。由于轴承结构的微小型化，工作载荷也趋向轻微，对轴承在微载荷下摩擦学特性的要求越来越高。微载荷下，结构，表面特性，载荷，速度和润滑剂等引起的微小激励都将使轴承的运转状态出现不稳定。摩擦稳定性已成为评价轴承性能的关键技术指标。通过理论分析和试验研究，探讨微载荷下含油轴承的摩擦学特性，从材料，结构，润滑方面探索提高轴承摩擦性能的途径，将丰富摩擦学的理论知识，并为满足日益增长的含油轴承的工程应用开拓途径。
本文运用含油轴承润滑理论和微载荷轴承摩擦试验技术，研究了多孔质材料的仿生设计，润滑特性的理论分析，微小摩擦量的检测技术，从理论和试验上全面揭示了微载荷下含油轴承的摩擦学特性和各种因素的影响规律。主要研究内容有：
1) 含油轴承的润滑机理：通过比较轴承润滑分析的Darcy模型，Slip-Flow模型和Brinkman模型，阐明了含油轴承润滑的物理过程，揭示影响轴承摩擦性能的因素。以毛细管效应，电磁场作用和热效应为重点，阐明了它们在含油轴承中的作用。
2) 微载荷含油轴承的摩擦特性：由于影响因素众多，微载荷下轴承的摩擦性能呈现明显的不稳定性。轴承的结构，载荷，摩擦，润滑性能都出现强随机性。微载荷下含油轴承的性能特征的追求已从以往的摩擦系数极小化转化为对摩擦参数稳定性的要求。
3) 多孔质材料的特性：运用SEM技术研究天然材料的多孔结构，通过对天然材料中多孔质的尺寸，几何构型，孔隙密度及其变化梯度的观测，划分均匀多孔质材料，梯度多孔质材料和复合多孔质材料。根据仿生原理，为含油轴承材料提出梯度型多孔质结构优化设计。
4) 含油轴承润滑的理论分析：基于Brinkman模型，用Elrod算法计算微载荷含油轴承的润滑状态，揭示多孔质材料中润滑油的渗透度对轴承性能的影响。发现大渗透度下，轴承几乎丧失承载能力，而渗透度小于一极限值时，对润滑影响的差别几乎可以忽略不计。一般渗透度条件下，摩擦系数随载荷的下降而上升，当载荷大到一极限值时摩擦系数趋向稳定值，并与试验结果相吻合。但是，试验中惯性引起的系统误差使计算得到的摩擦系数值小于测量值。
5) 微载荷含油轴承中的混沌研究：研究发现，微载荷含油轴承摩擦学系统为混沌系统。出现混沌现象的原因是与速度有关的摩擦力和与弹性有关的粘弹性共同作用的结果。鉴于微载荷含油轴承性能研究中摩擦稳定性的重要性，对①无摩擦，无驱动，②有摩擦，无驱动和③有摩擦，有驱动三种情况研究了轴承摩擦学混沌系统，得到了判别稳定性的条件。用随机函数作驱动项得到线性化摩擦系统的混沌表现。在线性化混沌方程和随机函数输入条件下，微载荷摩擦混沌现象表现为杂乱无章的速度与加速度关系。随着固体接触和固体摩擦成分的增加，速度与加速度关系表现出有规律的渐进稳定状态。
In appliances of IT and MEMS equipments, the tribological characteristics especially friction stability under micro-loads become key factors for the performances of porous bearings, but the study of these topics has not been carried out in the past. The friction performance under micro-load is defined as instability due to bearing configurations that include clearance, roughness, lubricants and velocity etc. after the load is small to some extent, and the unsteady state is a typical tribology character of bearings under micro-load. The goals of this dissertation are to investigate tribological performance factors, bionic porous design, measurement of friction coefficients and chaos state of friction of porous bearings under micro-load. The detail contents and results are as follows
1) The lubrication mechanism of porous bearing was discussed. And, Darcy model, Slip-flow model, Brinkman model and other models for lubrication were comparatively analyzed. The tribological factors and the experimental methods of porous bearings were reviewed. The lubricant property and surface topography of bearings under micro-load play largely influences on the tribological performances than those under general conditions. And, tribological performances under micro-load show comprehensive characteristics, and suggest the investigation necessity of the interactions between lubricants and friction surfaces, the lubrication capability etc., of which the requirement of lowest friction coefficient is replaced by friction stability.
2) The porous capillarity, magnetism distribution and/or its thermal effects are fundamental problems. The capillarity effects of porous bearings were analyzed and summarized, because the capillarity carries a part of hydrodynamic pressure in lubrication film. The electromagnetic effects on bearing functions should not be neglected under some cases. Thus, the distribution characters of magnetic field in journal bearings are obtained by FEM. And, the results show that an edge effect emerges at axial ends of bearings, and an aggregation effect appears at radial eccentricity. Hence, the above influences on bearings are not structural uniform. The eddy thermal effect in the rotating shaft can be neglected at low speeds but brings a temperature rise beyond 20℃ at high speeds, and the rise range of temperature ascends with the increase of speed.
3) Micro-pores structures of some natural materials were studied with SEM. The results show that the micro structures can be classified into three types, namely uniform pores, gradient pores and multi-pores in terms of the distribution variation of porous density, size and geometry. An optimal design of porous bearings was proposed based on the gradient configuration. For the structure design requiring coordination of strength, mass and vibration, bionic design has superiority to conventional methods.
4) Based on the Brinkman model, Elrod algorithm was used to compute the lubrication performances. The results show that permeability significantly influences friction coefficient for large permeability, and computed load is very trivial; the above influence difference can be neglected as permeability is smaller than a certain value. Under general permeability and mi-
本文运用含油轴承润滑理论和微载荷轴承摩擦试验技术，研究了多孔质材料的仿生设计，润滑特性的理论分析，微小摩擦量的检测技术，从理论和试验上全面揭示了微载荷下含油轴承的摩擦学特性和各种因素的影响规律。主要研究内容有：
1) 含油轴承的润滑机理：通过比较轴承润滑分析的Darcy模型，Slip-Flow模型和Brinkman模型，阐明了含油轴承润滑的物理过程，揭示影响轴承摩擦性能的因素。以毛细管效应，电磁场作用和热效应为重点，阐明了它们在含油轴承中的作用。
2) 微载荷含油轴承的摩擦特性：由于影响因素众多，微载荷下轴承的摩擦性能呈现明显的不稳定性。轴承的结构，载荷，摩擦，润滑性能都出现强随机性。微载荷下含油轴承的性能特征的追求已从以往的摩擦系数极小化转化为对摩擦参数稳定性的要求。
3) 多孔质材料的特性：运用SEM技术研究天然材料的多孔结构，通过对天然材料中多孔质的尺寸，几何构型，孔隙密度及其变化梯度的观测，划分均匀多孔质材料，梯度多孔质材料和复合多孔质材料。根据仿生原理，为含油轴承材料提出梯度型多孔质结构优化设计。
4) 含油轴承润滑的理论分析：基于Brinkman模型，用Elrod算法计算微载荷含油轴承的润滑状态，揭示多孔质材料中润滑油的渗透度对轴承性能的影响。发现大渗透度下，轴承几乎丧失承载能力，而渗透度小于一极限值时，对润滑影响的差别几乎可以忽略不计。一般渗透度条件下，摩擦系数随载荷的下降而上升，当载荷大到一极限值时摩擦系数趋向稳定值，并与试验结果相吻合。但是，试验中惯性引起的系统误差使计算得到的摩擦系数值小于测量值。
5) 微载荷含油轴承中的混沌研究：研究发现，微载荷含油轴承摩擦学系统为混沌系统。出现混沌现象的原因是与速度有关的摩擦力和与弹性有关的粘弹性共同作用的结果。鉴于微载荷含油轴承性能研究中摩擦稳定性的重要性，对①无摩擦，无驱动，②有摩擦，无驱动和③有摩擦，有驱动三种情况研究了轴承摩擦学混沌系统，得到了判别稳定性的条件。用随机函数作驱动项得到线性化摩擦系统的混沌表现。在线性化混沌方程和随机函数输入条件下，微载荷摩擦混沌现象表现为杂乱无章的速度与加速度关系。随着固体接触和固体摩擦成分的增加，速度与加速度关系表现出有规律的渐进稳定状态。
In appliances of IT and MEMS equipments, the tribological characteristics especially friction stability under micro-loads become key factors for the performances of porous bearings, but the study of these topics has not been carried out in the past. The friction performance under micro-load is defined as instability due to bearing configurations that include clearance, roughness, lubricants and velocity etc. after the load is small to some extent, and the unsteady state is a typical tribology character of bearings under micro-load. The goals of this dissertation are to investigate tribological performance factors, bionic porous design, measurement of friction coefficients and chaos state of friction of porous bearings under micro-load. The detail contents and results are as follows
1) The lubrication mechanism of porous bearing was discussed. And, Darcy model, Slip-flow model, Brinkman model and other models for lubrication were comparatively analyzed. The tribological factors and the experimental methods of porous bearings were reviewed. The lubricant property and surface topography of bearings under micro-load play largely influences on the tribological performances than those under general conditions. And, tribological performances under micro-load show comprehensive characteristics, and suggest the investigation necessity of the interactions between lubricants and friction surfaces, the lubrication capability etc., of which the requirement of lowest friction coefficient is replaced by friction stability.
2) The porous capillarity, magnetism distribution and/or its thermal effects are fundamental problems. The capillarity effects of porous bearings were analyzed and summarized, because the capillarity carries a part of hydrodynamic pressure in lubrication film. The electromagnetic effects on bearing functions should not be neglected under some cases. Thus, the distribution characters of magnetic field in journal bearings are obtained by FEM. And, the results show that an edge effect emerges at axial ends of bearings, and an aggregation effect appears at radial eccentricity. Hence, the above influences on bearings are not structural uniform. The eddy thermal effect in the rotating shaft can be neglected at low speeds but brings a temperature rise beyond 20℃ at high speeds, and the rise range of temperature ascends with the increase of speed.
3) Micro-pores structures of some natural materials were studied with SEM. The results show that the micro structures can be classified into three types, namely uniform pores, gradient pores and multi-pores in terms of the distribution variation of porous density, size and geometry. An optimal design of porous bearings was proposed based on the gradient configuration. For the structure design requiring coordination of strength, mass and vibration, bionic design has superiority to conventional methods.
4) Based on the Brinkman model, Elrod algorithm was used to compute the lubrication performances. The results show that permeability significantly influences friction coefficient for large permeability, and computed load is very trivial; the above influence difference can be neglected as permeability is smaller than a certain value. Under general permeability and mi-
引文
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88 Guglielmino A, Tadde AR. Fine structure of the eggshell of ommatissus binotatus fieber (homoptera, auchenorrhyncha, tropiduchidae). Insect Morphol and Embryol, 1997, 26 (2) : 85-89.
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103 Kitimasak W, Thirakhupf K, Moll DL. Eggshell structure of the Siamese Narrow-headed softshell turtle Chitra chitra Nutphand. Science Asia, 2003, 29: 95-98.
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105 朱震刚．金属泡沫材料研究．物理，1999，28(2)：84-88．
106 Maine EMA, Ashby MF. Applying the investment methodology for materials (IMM) to aluminum foams. Materials and Design, 2002, 23: 307-319.
107 Danielsson M, LGrenestedt J. Gradient foam core materials for sandwich structures: preparation and characterization. Composites(A), 1998, 29: 981-988.
108 Tichy JA. A porous medis model for thin film lubrication. Journal of Tribology, 1995, 117: 16-21.
109 li WL. Derivation of modified Reynolds equation-a porous media model. Journal of Tribology, 1999, 121: 823-829.
110 Aaron AJ, Ramagopal P. The impact of Brinkman's extension of Darcy's law in the neighborhood of a circular preferential flow pathway. Environmental Modeling & Software, 1999, 14: 427-435.
111 孙大成．润滑力学讲义．北京：中国友谊出版社，1991．
112 郑林庆．摩擦学原理．北京：高等教育出版社，1994．
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115 Jakobsson B, Floberg L. The finite journal bearing considering vaporization. Chalmers Tekniska Hoegskolas Handlingar, 1957, 190: 111-116.
116 Olsson KO. Cavitation in dynamically loaded bearing. Goteborg: Chalmers University of Technology, 1965.
117 Ochoa-Tapis JA, Whitaker A. Momentum tranfer at the boundary between a porous medium and a homogeneous fluid-Theoretical development. International Journal of Heat and Mass Transfer, 1995, 38: 2635-2646.
118 Vijayaraghavan D, Keith TG. Development and evaluation of a cavitation algorithm. STLE, Tribology Transactions, 1989, 31 (2) : 225-33.
119 Lorenz EN. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 1963, 20: 130-141.
120 黄润生．混沌及其应用．武汉：武汉大学出版社，2000．
121 Brown RD, Drummond G, Addison PS. Chaotic response of a short journal bearing. Journal of Engineering Tribology, 2000, 214 (4) : 387-400.
122 Wojewoda J, Kapitaniak T, Barton R, Brindley J. Complex behaviour of a quasiperiodically forced experimental system with dry friction. Chaos, Solitons and Fractals, 1993, 3 (1) : 35-46.
123 Cheng G, Zu JW. Dynamics of a dry friction oscillator under two-frequency excitations. Journal of Sound and Vibration, 2004, 275: 591-603.
124 Bharathia MS, Ananthakrishnaa G. Possibility of chaos in internal friction experiments of martensites. Physica A, 1999, 270: 159-164.
125 Awrejcewicz J, Sendkowski D. How to predict stick-slip chaos in R4. Physics Letters A, 2004, 330: 371-376.
126 Fitsum AT, Robert JR. Improved dynamic friction models for simulation of one-dimensional and two-dimensional stick-slip motion. Journal of Tribology, 2001, 123: 661-670.
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