Calculation of Tilting Pad Bearing Forces

In the field of rotor dynamics, developing dynamic models is essential for analyzing the vibrations of different types of machines under various operating conditions. These models enable early fault detection and facilitate predictive maintenance, thus extending the system’s lifespan and reducing unplanned downtime. However, modeling vertical rotors presents additional challenges. Unlike hori- zontal rotors, the shaft position in vertical rotors constantly varies, complicating numerical simulations. Furthermore, in the case of tilting-pad bearings, which are most commonly used in this configuration, no model is available that accurately estimates the hydrodynamic forces, which significantly influence rotor motion. In this study, a new methodology was developed to determine the dynamic behavior of a vertical rotor. To achieve this, a new model was proposed to describe the dynamic behavior of tilting-pad bea- rings. Expressions were formulated to calculate the hydrodynamic force in these bearings based on the geometry and fluid behavior. A formula was developed to determine the oil film thickness, allowing for a more accurate solution of the Reynolds equation.在转子动力学领域，构建动力学模型是分析各类设备在不同运行工况下振动特性的必要手段。此类模型可实现早期故障检测，助力预测性维护，进而延长系统使用寿命并减少非计划停机时长。 然而，立式转子的建模工作存在额外挑战。与卧式转子不同，立式转子的轴颈位置持续变化，这使得数值模拟的复杂度显著提升。此外，该配置中最常用的可倾瓦轴承（tilting-pad bearings），目前尚无模型能够准确估算对转子运动具有显著影响的流体动载荷。 本研究提出了一种用于分析立式转子动力学特性的全新方法。为此，我们构建了可倾瓦轴承动力学特性的全新描述模型。基于轴承几何参数与流体流动特性，推导得到了此类轴承流体动载荷的计算表达式。同时，提出了油膜厚度的求解公式，可实现雷诺方程（Reynolds equation）的更精准求解。