日常接觸行為多伴隨瞬間衝擊與回彈，使潤滑油膜在極短時間內承受快速擠壓與剪切，導致剪切速率劇烈變化，因此難以以黏度為常數的牛頓流體假設完整描述。實際潤滑劑常呈現剪切稀化等非牛頓特性，並可能具有近似降伏行為，使黏度隨剪切條件改變而影響承載能力與膜厚穩定性；若仍採用牛頓流體假設，容易低估衝擊液動潤滑下的油膜阻抗，而直接採用理想降伏模型又可能在低剪切區造成數值不穩定。本研究採用雙黏度模型以連續方式描述低剪切與高剪切區之黏度轉換，並建立衝擊彈塑性液動潤滑之暫態耦合分析，藉由同時求解暫態修正雷諾方程式、負載平衡方程式與球體運動方程式，系統性探討接觸壓力與膜厚變化以及固體變形之交互影響。
黏度比降低時油膜緩衝能力下降，使承載分攤更容易往徑向外擴、最小膜厚位置外移且油膜更薄，並在彈塑性條件下提高固體耗散比例而促進塑性累積與殘留凹陷加深；反之，較高黏度比可使承載更集中並維持較厚且較穩定的油膜，有助於抑制塑性區擴展與降低殘留變形。本研究的主要貢獻在於推導出可納入雙黏度流變條件且包含牛頓流體特例的泛用雷諾方程式，提供衝擊潤滑問題下雙黏度流體之分析基礎。

In many practical contacts are often accompanied by instantaneous impact and rebound processes, during which the lubricant film is subjected to rapid squeeze and shear within a very short time. This leads to drastic variations in shear rate, making it difficult to be fully captured by the Newtonian assumption of constant viscosity. Practical lubricants commonly exhibit non-Newtonian behaviors such as shear thinning and may present yield-like characteristics, whereby viscosity changes with shear conditions and consequently affects load-carrying capacity and film-thickness stability. If the Newtonian assumption is still adopted, the film resistance under impact elastohydrodynamic lubrication (EHL) is likely to be underestimated, whereas directly applying an ideal yield model may cause numerical instability in low-shear regions. In this study, a bi-viscosity model is employed to continuously represent the viscosity transition between low- and high-shear regions. A transient coupled analysis of impact plasto-elastohydrodynamic lubrication is established by simultaneously solving the transient modified Reynolds equation, the load-balance equation, and the equation of motion of the ball, in order to systematically investigate the interactions among contact pressure, film-thickness variation, and solid deformation.
The results show that, as the viscosity ratio decreases, the cushioning effect of the lubricant film weakens, causing the load-sharing to shift outward in the radial direction, the minimum film-thickness location to move outward, and the film to become thinner. Under elastic–plastic conditions, a lower viscosity ratio also increases the fraction of solid dissipation, promoting plastic accumulation and resulting in deeper residual indentations. In contrast, a higher viscosity ratio leads to more concentrated load support and maintains a thicker and more stable lubricant film, which helps suppress the expansion of the plastic zone and reduce residual deformation. The main contribution of this study lies in deriving a general Reynolds equation that incorporates bi-viscosity rheology while encompassing the Newtonian limit, providing a fundamental framework for analyzing bi-viscosity lubricants in impact lubrication problems.

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