Lubricants can exhibit significant viscoelastic effects due to the addition of high molecular weight polymers. The overall behavior of the mixture is vastly different from a simpler Newtonian fluid. Therefore, understating the influence of viscoelasticity on the load carrying capacity of the film is essential for lubricated contacts. A new modeling technique based on lubrication theory is proposed to take into account viscoelastic effects. As a result, we obtain a modified equation for the pressure, i.e. the viscoelastic Reynolds (VR) equation. We have first examined a parabolic slider to mimic a roller bearing configuration. An increase of the load carrying capacity is observed when polymers are added to the lubricant. Furthermore, our results are compared with existing models based on the lubrication approximation and direct numerical simulations (DNS). For small Weissenberg number ($Wi$), i.e. the ratio between the polymer relaxation time and the residence time scale, VR predicts the same pressure of the linearized model, in which $ϵWi$ is the perturbation parameter ($ϵ$ is the ratio between the vertical length scale and the horizontal length scale). However, the difference grows rapidly as viscoelastic effects become stronger. Excellent quantitative and qualitative agreement is observed between DNS and our model over small to moderate Weissenberg number. While DNS is numerically unstable at high values of the Weissenberg number, VR does not have the same issue allowing to capture the evolution of the stress and pressure also when the viscoelastic effects are strong. It is shown that even in high shear flows, normal stresses have the largest impact on load carrying capacity and thus cannot be neglected. Furthermore, the additional pressure due to viscoelasticity comprises two components, the first one due to the normal stress and the second one due to the shear stress. Afterwards, the methodology used for the parabolic slider is extended to a plane slider where, instead, the load decreases by adding polymers to the fluid. In particular, under the effect of the polymers surface slopes enhance the rate at which pressure gradients increase, whereas curvature opposes this along the contact. Therefore, the increase of the load carrying capacity observed for viscoelastic lubricants is due to its shape close to the inlet, which is steeper than the plane slider.

由于添加了高分子量聚合物，润滑剂可能会表现出显着的粘弹性效应。混合物的整体行为与较简单的牛顿流体有很大不同。因此，对于润滑触点而言，低估粘弹性对薄膜的承载能力的影响至关重要。考虑到粘弹性效应，提出了一种基于润滑理论的新建模技术。结果，我们获得了压力的修正方程，即粘弹性雷诺（VR）方程。我们首先研究了抛物线形滑块，以模拟滚子轴承的构造。当将聚合物添加到润滑剂中时，观察到承载能力的增加。此外，我们的结果与基于润滑近似和直接数值模拟（DNS）的现有模型进行了比较。对于较小的魏森伯格数（$\mathrm{w\; ^}\mathrm{一世}$），即聚合物弛豫时间与停留时间比例之间的比率，VR预测线性化模型的压力相同，其中 $ϵ\mathrm{w\; ^}\mathrm{一世}$ 是摄动参数（$ϵ$是垂直长度刻度和水平长度刻度之间的比率）。但是，随着粘弹性作用变得越来越强，差异迅速增大。在小到中等的Weissenberg数上，DNS和我们的模型之间观察到了极好的定量和定性协议。尽管DNS在Weissenberg数的高值上在数值上不稳定，但是VR并没有相同的问题，即使在粘弹效应很强的情况下，VR也可以捕获应力和压力的变化。结果表明，即使在高剪切流中，法向应力对承载能力的影响最大，因此不能忽略。此外，由于粘弹性而产生的附加压力包括两个分量，第一个分量归因于法向应力，第二个分量归因于剪切应力。然后，抛物线滑块所使用的方法扩展到平面滑块，而在平面滑块中，通过向流体中添加聚合物来降低载荷。特别地，在聚合物的作用下，表面斜率增加了压力梯度增加的速率，而曲率沿接触相反。因此，对于粘弹性润滑剂观察到的承载能力的增加是由于其形状靠近入口，其形状比平面滑块要陡。