By using the couple-stress elasticity theory, this article firstly analyzes the size-dependent elastohydrodynamic lubrication (EHL) line contact between a deformable half-plane and a rigid cylindrical punch. The size effect that emerged from the material microstructures is described by the characteristic material length. It is assumed that the viscosity and density of the lubricant vary with the fluid pressure. An iterative method is developed to deal with the flow rheology equation, film thickness equation, load balance equation and Reynolds equation at the same time. Then, distributions of fluid pressure, in-plane stress and film thickness are determined numerically at the lubricant contact surface. Influences of the size parameter, punch radius, resultant normal load and entraining velocity on the fluid pressure, in-plane stress and lubricant film thickness are discussed. The fluid pressure and film thickness predicted from the couple-stress elasticity theory present significant departures from the classical elasticity results. It is demonstrated that results for micro-/nano-scale EHL contact problems may be underestimated when the classical elasticity theory is employed.

利用偶应力弹性理论，本文首先分析了可变形半平面与刚性圆柱冲头之间尺寸相关的弹性流体动力润滑（EHL）线接触。由材料微观结构产生的尺寸效应由材料的特征长度来描述。假定润滑剂的粘度和密度随流体压力而变化。提出了一种同时处理流变方程，膜厚方程，载荷平衡方程和雷诺方程的迭代方法。然后，在润滑剂接触表面处数值确定流体压力，面内应力和膜厚度的分布。尺寸参数，冲头半径，合成法向载荷和夹带速度对流体压力的影响，讨论了平面应力和润滑膜厚度。根据偶合应力弹性理论预测的流体压力和膜厚与经典弹性结果有很大的出入。结果表明，采用经典弹性理论时，可能会低估微观/纳米级EHL接触问题的结果。