To make a deep investigation into the lubrication characteristics of the liquid metal film (LMF), the existing 2-D hydrodynamic lubrication models cannot meet the requirement as it fails to describe the flow of the liquid film at the transverse direction. This article makes the first step toward a 3-D model of the LMF at the armature/rail (A/R) interface. A 2-D Reynolds equation is derived considering the self-acceleration of the film and the Lorentz force acting on it. By coupling the electromagnetic fields, stress, and fluid fields, a magneto-elastohydrodynamic model is established completely. Based on this, the distribution characteristics of the LMF are explored which includes the distribution of the film thickness, hydrodynamic pressure, and fluid velocity. Besides, the dynamic characteristics of the LMF in the launch process are analyzed. The results show that: 1) the LMF is trapped in an arching gap in the transverse direction. The liquid pressure is symmetrically distributed along the centerline. In addition, the positive transverse fluid velocity indicates the jetting of the molten metal which may do damage to the bore. 2) At the current down-slope, the film thickness and liquid pressure both decrease rapidly which may put the film at risk of break. This article can provide a reference to the modeling of LMF hydrodynamic lubrication and help to understand the flow behavior of the liquid film.

中文翻译：

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轨道-电枢界面处液态金属膜的 3-D 磁弹性流体动力学模型

为了深入研究液态金属膜（LMF）的润滑特性，现有的二维流体动力润滑模型无法描述液膜横向流动，无法满足要求。本文迈出了在电枢/导轨 (A/R) 接口处建立 LMF 3-D 模型的第一步。考虑到薄膜的自加速和作用在其上的洛伦兹力，推导出二维雷诺方程。通过耦合电磁场、应力和流体场，完整地建立了磁弹流体动力学模型。在此基础上，探索了LMF的分布特性，包括膜厚、流体动压和流体速度的分布。此外，分析了发射过程中LMF的动态特性。结果表明：1）LMF被困在横向的拱形间隙中。液体压力沿中心线对称分布。此外，正的横向流体速度表示可能对孔造成损坏的熔融金属的喷射。2）在目前的下坡处，油膜厚度和液体压力都迅速下降，可能会使膜有破裂的风险。本文可为LMF流体动力润滑建模提供参考，有助于理解液膜的流动行为。2）在目前的下坡处，油膜厚度和液体压力都迅速下降，可能会使膜有破裂的风险。本文可为LMF流体动力润滑建模提供参考，有助于理解液膜的流动行为。2）在目前的下坡处，油膜厚度和液体压力都迅速下降，可能会使膜有破裂的风险。本文可为LMF流体动力润滑建模提供参考，有助于理解液膜的流动行为。