Combined Explicit Finite and Discrete Element Methods for Rotor Bearing Dynamic Modeling

Abstract

This article presents a new approach in which the explicit finite element method (EFEM) and the discrete element method (DEM) are coupled to investigate dynamics of flexible rotor systems supported by deep-groove ball bearings. In this investigation, DEM is used to develop the bearing (dynamic motion) model in which all of the components of the bearing (i.e., inner and outer race, balls, and cage) have 6 degrees of freedom. The flexible shaft is modeled with a full 3D elastic formulation using the EFEM rather than the reduced form, which implements component mode synthesis. The EFEM and DEM were combined to investigate the dynamics of flexible shaft rotor systems supported by ball bearings. Rotor and inner races of the bearings are fully coupled such that both translation and rotation of the flexible rotor are transmitted to the bearings. At each time step, the translational motion and rotation/tilt angle of the rotor cross section at the location of an inner race are applied to the inner race of the bearing. The resulting reaction forces and moments calculated in the dynamic bearing model are in turn applied to the nodes of the shaft. The combined model is used to investigate the motions of the inner races and the resulting reaction forces and moments from the supporting bearings due to an applied load on the shaft. In the current coupled modeling approach, the deformation of the shaft affects the internal components of the bearing by altering the orientation of the inner race, which results in ball spin and slip.

An overview of dynamic modeling of rolling-element bearings

“…30–53 This inadequacy has been solved by finite element (FE) models and simulation software packages. 54–59 Furthermore, FE and discrete element methods were united to model a fully coupled flexible rotor-bearing system dynamically. This modeling requires explicit knowledge of a physical system and finite theory.…”

“…This modeling requires explicit knowledge of a physical system and finite theory. 58,59 A distinctive vector bond graph method was adopted to model REB with faults. This shows a graphical representation of the free-body diagram of bearing elements and their association.…”

“…Degrees of freedom (DOFs) of bearing components had been a key aspect to develop dynamic models of REB. From basic two-dimensional (2D) models related to the motion of rolling element 30,32,33,37 to full 6-DOF models with consideration of flexibly structured cage 31,34,35,38–40,45,46,51,56–58 have been developed to resolve the dynamic equations of bearing motion. Also, lubricant traction characteristics between the contact areas are one of the crucial aspects of the dynamic behavior of REB.…”

Dynamic Analysis of Flexible Rotor Based on Transfer Symplectic Matrix

“…e expression of the rotor finite element method is concise and standard, which has prominent advantages when solving the problems of the large complex system composed of rotor and surrounding structures, but this method will increase the system freedom degree and result in a lot of time and space spending [5][6][7].…”

Vibration modes of the rotor system of turbocharger with floating-ring bearing

“…The different types of vibration problems of rotor system have been studied [1][2][3][4][5][6][7][8][9][10]. For example, Ying J.…”