雷诺方程(英語:Reynolds equation)是流体润滑理论中的基本方程,描述流体薄膜的压力分布,可由纳维-斯托克斯方程导出。该方程由英国物理学家奥斯鲍恩·雷诺于1886年提出。[1]
雷诺方程的导出建立在以下假设的基础之上:
- 流体为牛顿流体
- 黏性力远大于惯性力,即雷诺数十分小
- 体积力可以忽略
- 压力沿厚度方向基本不变(
)
- 流体膜厚度远小于宽度与长度(
及
)
雷诺方程的表达式为:[2][3]
![{\displaystyle {\frac {\partial }{\partial x}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial x}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial y}}\right)={\frac {\partial }{\partial x}}\left({\frac {\rho h\left(u_{a}+u_{b}\right)}{2}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h\left(v_{a}+v_{b}\right)}{2}}\right)+\rho \left(w_{a}-w_{b}\right)-\rho u_{a}{\frac {\partial h}{\partial x}}-\rho v_{a}{\frac {\partial h}{\partial y}}+h{\frac {\partial \rho }{\partial t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28714e9cecdd356e024792482e4ee6ebfff72c4a)
其中
为流体膜压力,
与
为流体轴承宽度与长度方向坐标,
为流体膜厚度方向坐标,
为流体膜厚度,
为流体黏度,
为流体密度,
分别为
方向的边界速度,
则分别表示上、下边界。
- ^ 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.[1]
- ^ Fundamentals of Fluid Film Lubrication. Hamrock, B., Schmid, S., Jacobson. B. 2nd Edition. 2004. ISBN 0-8247-5371-2
- ^ Fluid Film Lubrication. Szeri, A. 2nd Edition. 2010. ISBN 0521898234.