Improvement of the numerical efficiency of rotordynamic simulations by applying the Scaled Boundary Finite Element Method to compute the hydrodynamic bearings

通过应用比例边界有限元法计算流体动压轴承来提高转子动力学模拟的数值效率

• 批准号: 490625563
• 负责人: Professor Dr.-Ing. Elmar Woschke
• 金额: --
• 依托单位: Institut für Mechanik (IFME)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/490625563?language=en
• 关键词: Improvement; numerical; efficiency; rotordynamic; simulations

The rotordynamic properties of systems with hydrodynamic bearings are affected crucially by the nonlinear bearing forces. Regarding fast-rotating, lightly-loaded rotors, this causes subsynchronous self-excited oscillations with potentially high amplitudes, which can reduce the durability of the components, cause critical noise emissions, and affect the energy efficiency of the machine. To reduce expensive test bench experiments and time-consuming iterations in the product development process, the design has to be based on precise simulative analyses of the operating behavior under consideration of the nonlinear interactions between the bearing forces and the shaft vibrations. To this end, the equation of motion of the elastic shaft is incorporated into a time integration scheme and coupled with the Reynolds equation, which describes the pressure generation in hydrodynamic bearings. Hence, each time step of the simulation includes a solution of the Reynolds equation, for which numerical methods, analytical approximations, and look-up tables are employed. While numerical methods lead to considerable and often inacceptable computational times, analytical solutions are only possible in conjunction with substantial simplifications. The look-up table approach, to some extent, offers a tradeoff between these two extremes, while the modeling depth is usually limited, since the interpolation effort increases with every considered physical effect.A promising basis for the development of a novel, numerically efficient solution without the substantial limitations of analytical methods or look-up table techniques is the semi-analytical Scaled Boundary Finite Element Method (SBFEM). The fundamentals for solving the Reynolds equation with the SBFEM have been derived in preliminary work, but the potential of the approach has not been exploited yet, which is the objective of this project. In order to further reduce the numerical effort, high-order shape functions need to be employed in combination with an automatic, adaptive mesh refinement as well as coarsening and a transformation of the Reynolds equation in a manner that smoothens the solution is analyzed. Another strategy worth investigating is to avoid the repeated solution of eigenvalue problems within the time integration scheme. This requires that the eigenvalue problem is differentiated with respect to the parameters of the shaft displacement and developed into a series prior to the rotordynamic simulation. In order to improve the modeling depth of the SBFEM solution compared to the preliminary work, strategies for incorporating mass-conserving cavitation models as well as shaft tilting need to be investigated. In the last step, the developed methodology is to be verified and analyzed with regard to its efficiency. To ensure a realistic context, this is done within the framework of a rotor dynamics or MBS formulation, whereby complex technical overall systems can also be simulated.

具有流体动压轴承的系统的转子动力学特性受到非线性轴承力的严重影响。对于快速旋转、轻载的转子，这会导致具有潜在高振幅的次同步自激振荡，从而降低部件的耐用性，导致严重的噪声排放，并影响机器的能源效率。为了减少产品开发过程中昂贵的测试台实验和耗时的迭代，设计必须基于对运行行为的精确模拟分析，同时考虑轴承力和轴振动之间的非线性相互作用。为此，弹性轴的运动方程被纳入时间积分方案中，并与描述流体动压轴承中压力产生的雷诺方程耦合。因此，模拟的每个时间步长都包含雷诺方程的解，为此采用了数值方法、解析近似和查找表。虽然数值方法会导致相当多且通常不可接受的计算时间，但解析解只有与大量简化相结合才可能实现。查找表方法在某种程度上提供了这两个极端之间的权衡，而建模深度通常是有限的，因为插值工作量随着每一个考虑的物理效应的增加而增加。半解析尺度边界有限元法（SBFEM）是开发新颖的、数值有效的解决方案的一个有希望的基础，而不受分析方法或查找表技术的实质性限制。使用 SBFEM 求解雷诺方程的基本原理已在前期工作中得出，但该方法的潜力尚未得到开发，而这正是该项目的目标。为了进一步减少数值工作，需要将高阶形状函数与自动、自适应网格细化以及粗化结合使用，并以平滑解的方式分析雷诺方程的变换。另一个值得研究的策略是避免在时间积分方案中重复求解特征值问题。这要求在转子动力学仿真之前将特征值问题相对于轴位移的参数进行微分并发展成级数。与前期工作相比，为了提高 SBFEM 解决方案的建模深度，需要研究结合质量守恒空化模型和轴倾斜的策略。最后一步，将对所开发的方法的效率进行验证和分析。为了确保真实的背景，这是在转子动力学或 MBS 公式的框架内完成的，由此还可以模拟复杂的技术整体系统。