Lubricating oils are used to minimize the friction and wear of mechanical components by virtue of a thin lubricant film separating the sliding surfaces. The film’s characteristics, under high pressure, can exhibit non-Newtonian effects, such as viscoelasticity and shear thinning. The strength of these effects are measured using the Weissenberg (Deborah) number $Wi$ ($De$), i.e., the ratio of the polymer relaxation time to the shear (residence) time scale. Modeling these effects is computationally challenging, especially when relying on the direct numerical simulation (DNS) of the Cauchy momentum and the mass conservation equations. However, the viscoelastic Reynolds (VR) approach (Ahmed & Biancofiore, Journal of Non-Newtonian Fluid Mechanics, 292, 104524, 2021.) has been shown to be effective in modeling (i) the pressure distribution and (ii) the load carrying capacity of a viscoelastic lubricating film for mechanical contacts for the Oldroyd-B constitutive relation, since these contacts operate within the small $De$ limit (but no constraint in $Wi$). In this work, we have extended the VR approach to the finitely extensible non-linear elastic (FENE) type constitutive relations that account for the (i) finite extension of the polymer chains and (ii) shear thinning. We have validated the VR approach against DNS, showing an excellent agreement over a wide range of the Weissenberg number $Wi$, and finite extensibility parameter $L$, using FENE-CR and FENE-P models. Following a thorough validation, the pressure distribution and the load carrying capacity of a journal bearing, whose channel height is governed by the journal eccentricity ratio $e$, is considered. It is observed that the load carrying capacity of the film portrays a strongly non-linear dependence on $Wi$, $L$ and $e$: while it increases for small values of $Wi$, limited greatly by the capacity of the polymer to stretch, a saturation and a subsequent decline is observed for high $Wi$ regimes. Additionally, a weakly (strongly) eccentric configuration plays an important role in promoting (hindering) the growth in load versus both $Wi$ and $L$. These effects are significant and have to be considered when modeling thin contacts lubricated with a strongly viscoelastic fluid.

润滑油通过分隔滑动表面的薄润滑油膜来最大限度地减少机械部件的摩擦和磨损。该薄膜的特性在高压下可以表现出非牛顿效应，例如粘弹性和剪切稀化。这些效应的强度是使用韦森伯格（黛博拉）数来衡量的$瓦我$（$De$），即聚合物弛豫时间与剪切（停留）时间尺度的比率。对这些效应进行建模在计算上具有挑战性，尤其是在依赖柯西动量和质量守恒方程的直接数值模拟(DNS) 时。然而，粘弹性雷诺 (VR) 方法（Ahmed & Biancofiore, Journal of Non-Newtonian Fluid Mechanics, 292, 104524, 2021.）已被证明可以有效地模拟 (i) 压力分布和 (ii) 承载用于 Oldroyd-B 本构关系的机械接触的粘弹性润滑膜的能力，因为这些接触在很小的范围内工作$De$限制（但没有限制$瓦我$）。在这项工作中，我们将 VR 方法扩展到有限可扩展非线性弹性 (FENE) 型本构关系，该关系解释了 (i) 聚合物链的有限延伸和 (ii) 剪切稀化。我们已经针对 DNS 验证了 VR 方法，在广泛的 Weissenberg 数范围内表现出极好的一致性$瓦我$，和有限可扩展性参数$L$，使用 FENE-CR 和 FENE-P 型号。经过彻底验证后，轴颈轴承的压力分布和承载能力（通道高度由轴颈偏心率决定）$e$， 被认为。据观察，薄膜的承载能力表现出强烈的非线性依赖性$瓦我$,$L$和$e$：虽然它会随着较小的值而增加$瓦我$，很大程度上受到聚合物拉伸能力的限制，观察到高饱和度和随后的下降$瓦我$政权。此外，弱（强）偏心配置在促进（阻碍）载荷增长方面发挥着重要作用$瓦我$和$L$。这些影响非常显着，在对用强粘弹性流体润滑的薄接触进行建模时必须考虑这些影响。