摘要
应用多重网格法求解稳态等温线接触弹性流体动力润滑(EHL)问题,得到了不同工况下使用不同的差分格式并采用不同的网格时的数值解。分析了对Reynolds方程的楔形项使用不同的差分格式时,数值解随着网格层数增加的变化趋势。结果表明:各种常见工况下,对楔形项无论是采用两点差分还是三点差分,随着网格层数的增加,得到的最小膜厚、中心膜厚、第二压力峰值及其出现的位置都会趋于稳定。由数值解归纳出了准确计算中心膜厚与最小膜厚的经验公式。网格层数较少时,将对楔形项分别采用两点差分和三点差分而得到的膜厚代入该公式,即可求出与网格层数较多时的结果非常接近的膜厚值。
The multi-grid method with various grids and different finite difference schemes was employed for the numerical solution of the steady-state isothermal elastohydrodynamic lubrication （EHL） in line contacts under different operating conditions. The variation of the numerical solutions versus the grid-level numbers and the influence of the finite difference schemes against the wedge term in the Reynlods equation on the numerical solutions were analysed. The results show that under ordinary operation conditions,with the increase of the grid-level number, both the central and minimum film thicknesses and both the height and position of the pressure spike become stable no matter two-point or three-point difference scheme was applied to the wedge term. Empirical formulas were derived for the accurate central and minimum film thicknesses Substituting the film thicknesses predicted by the multi-grid solvers with both two-point and three-point difference schemes but using less grid levels into the empirical formulas, the accurate film thicknesses, which are very close to those predicted by the corresponding solvers with much more grid levels, can be achieved easily.
出处
《润滑与密封》
CAS
CSCD
北大核心
2010年第4期5-9,共5页
Lubrication Engineering
基金
国家自然科学基金资助项目(50705045)
关键词
弹流膜厚
多重网格法
差分格式
经验公式
EHL film thickness
multi-grid method
finite difference scheme
empirical formula
