PSI - Issue 24

2

Vincenzo D’Addio et al. / Procedia Structural Integrity 24 (2019) 510–525 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

511

Peer-review under responsibility of the AIAS2019 organizers

Keywords: Rotordynamics; Campbell diagram; Finite element simulation; Multibody simulation; Ball bearing faults

1. Introduction The study of rotor dynamics is important in application areas that involve rotating machinery such as compressors, pumps, electric motors, steam or gas turbines and so on and plays an important role for improving safety and performances of the entire systems that they are part of. Unbalance or synchronous load can cause misfunctioning or even catastrophic failure at critical speeds. Even asynchronous loads can be dangerous for the durability of the components, especially bearings, if they excite some precessional modes of the shaft or vibration modes of the structure. For these reasons, simulating the behavior of a rotating machine with models and computational devices has an important role because it allows to predict critical speeds and to evaluate the effects of instabilities, saving time and money during the design phase, reducing the need of performing many experimental tests and of manufacturing physical prototypes. In the literature there are plenty of analytical and numerical studies of the dynamic behavior of rotating machinery and many excellent specialized text-books such as for example those by Krämer (1993), Ehrich (1998) and Genta (2005) and turbomachinery manufacturing companies have been using devoted software for predicting rotor performance for years. Smaller companies or companies with a broader scope of application, such as automotive components manufacturers, are less familiar with rotor dynamic analysis and have general purpose software. Analytical models are usually employed by researchers to investigate the dynamic behavior of simplified structures to highlight particular phenomena and obtain qualitative information as in Childs (1993) but quantitative information can be obtained only with more realistic models such as those based on the Finite Element Method (FEM) as described by Kirchgaßner (2016). Examples of such models are the flexible shaft with lumped masses and supports devised by Jung et al. (2014) for the rotordynamic FEM analysis of a radial inflow turbine and by Longxi et al. (2017) for the optimization of an aeroengine rotor system combining FEM rotordynamics calculation with a multidisciplinary optimization software. Vibration sources can be quite different and are usually simulated by exciting forces at specific frequencies as for defected rolling bearings. In recent years more attention has been given to modelling rolling element bearing fault in rotor-bearing-casing system by integrating FE models with lumped parameter ones and non linear bearing characteristics as done by Yang et al. (2018) and by means of a 3D multibody simulation software by Mishra et al. (2017). The present work is aimed at showing how different methodologies, such as analytical modelling, finite element, and multibody simulation, using commercial general-purpose software, can be adopted and integrated in both preliminary and detailed design phases. The study focuses on the rotordynamic analysis of a centrifugal pump for automotive applications motivated by the pump high rotational speed. In the next sections a brief description of the employed methodologies are briefly described, showing their advantages and limitations.

Nomenclature a

acceleration

a 1 ,a 2 BFS

distance of bearings 1 and 2 from center of mass

frequency of the ball passing on a point of the inner and outer race alternatively

BPFO frequency of the ball passing on a point of the outer race BPFI frequency of the ball passing on a point of the inner race BW backward C, ̌ damping matrix, complete and reduced d bearing ball diameter D bearing pitch diameter e eccentricity f, f 0 frequency, dimensionless frequency = f/f 0