| Homogenization of Reynolds Equation by Two-Scale Convergence |
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| 作者姓名： | Peter WALL |
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| 作者单位： | Department of |
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| 摘 要： | To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering-oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented.
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| 关 键 词： | 雷诺方程 均质化 两级收敛 润滑 |
| 收稿时间： | 9 May 2005 |
Homogenization of Reynolds Equation by Two-Scale Convergence |
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| Peter WALL.Homogenization of Reynolds Equation by Two-Scale Convergence[J].Chinese Annals of Mathematics,Series B,2007,28(3):363-374. |
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| Authors: | Peter WALL |
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| Institution: | Department of Mathematics,Luleà University of Technology,8-971 87 Lule(a),Sweden |
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| Abstract: | To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering-oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented. |
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| Keywords: | Homogenization Two-scale convergence Reynolds equation Lubrication |
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