A General Method for the Dynamic Modeling of Ball Bearing–Rotor Systems

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Yamin Li ◽  
Hongrui Cao ◽  
Linkai Niu ◽  
Xiaoliang Jin
Keyword(s):  
Rigid Body ◽  
Dynamic Modeling ◽  
Ball Bearing ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Rotor System ◽  
Body Motion ◽  
Rotor Systems ◽  
Proposed Model ◽  
Vibration Responses

A general dynamic modeling method of ball bearing–rotor systems is proposed. Gupta's bearing model is applied to predict the rigid body motion of the system considering the three-dimensional motions of each part (i.e., outer ring, inner ring, ball, and rotor), lubrication tractions, and bearing clearances. The finite element method is used to model the elastic deformation of the rotor. The dynamic model of the whole ball bearing–rotor system is proposed by integrating the rigid body motion and the elastic vibration of the rotor. An experiment is conducted on a test rig of rotor supported by two angular contact ball bearings. The simulation results are compared with the measured vibration responses to validate the proposed model. Good agreements show the accuracy of the proposed model and its ability to predict the dynamic behavior of ball bearing–rotor systems. Based on the proposed model, vibration responses of a two bearing–rotor system under different bearing clearances were simulated and their characteristics were discussed. The proposed model may provide guidance for structural optimization, fault diagnosis, dynamic balancing, and other applications.

A New Dynamic Model of Ball-Bearing Rotor Systems Based on Rigid Body Element

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Hongrui Cao ◽  
Yamin Li ◽  
Xuefeng Chen
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Ball Bearing ◽  
Rotor System ◽  
Radial Clearance ◽  
Fe Model ◽  
Ball Bearings ◽  
Rolling Ball ◽  
Rotor Systems ◽  
Body Element

Ball-bearing rotor systems are key components of rotating machinery. In this work, a new dynamic modeling method for ball-bearing rotor systems is proposed based on rigid body element (RBE). First, the concept of RBE is given, and then the rotor is divided into several discrete RBEs. Every two adjacent RBEs are connected by imaginary springs, whose stiffness is calculated according to properties of the RBEs. Second, all the parts of rolling ball bearings (i.e., outer ring, inner ring, ball, and cage) are considered as RBEs, and Gupta's model is employed to model bearings which include radial clearance, waviness, pedestal effect, etc. Finally, the rotor and all the rolling ball bearings are coupled to develop a dynamic model of the ball-bearing rotor system. The vibration responses of the ball-bearing rotor system can be calculated by solving dynamic equations of each RBE. The proposed method is verified with both simulation and experiment. The RBE model of the rotor is compared with its finite element (FE) model first, and numerical simulation shows the validity of the RBE model. Then, experiments are conducted on a rotor test rig which is supported with two rolling ball bearings as well. Good agreements between measurement and simulation show the ability of the model to predict the dynamic behavior of ball-bearing rotor systems.

Vibration of Moving Flexible Bodies (Formulation of Dynamics by Using Normal Modes and a Local Observer Frame)

1999 ◽  
Author(s):  
Atsushi Kawamoto ◽  
Mizuho Inagaki ◽  
Takayuki Aoyama ◽  
Nobuyuki Mori ◽  
Kimihiko Yasuda
Keyword(s):  
Rigid Body ◽  
Elastic Deformation ◽  
Multibody Systems ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Flexible Multibody ◽  
Local Observer ◽  
New Formulation

Abstract This paper deals with the formulation that can analyze vibration noise problems practically in the flexible multibody systems. Many kinds of formulations have been proposed on the flexible multibody systems so far. They are categorized into several groups according to their purposes and coordinate systems. The floating frame of reference formulation is at present the most popular method for general purpose simulations among them. The formulation uses Cartesian coordinates for the position of a body, Euler angles or Euler parameters for the orientations, and modal coordinates for the elastic degrees of freedom. The equations of motion with these different kinds of coordinates are complicated because of coupling between rigid body motion and elastic vibration. On the other hand, the linear theory of elasto-dynamics appears to be simple and could be practical for some limited uses. But it neglects the effect of the elastic deformation on the rigid body motion. In many cases, the effect is significant and essential. In this paper, we propose a new formulation with rigid body modes and a local observer frame (LOF) for large amplitude rigid body motion, and with elastic modes for small amplitude elastic vibration. The LOF is updated properly to compensate the gap between rigid body motion and the LOF motion. The new formulation makes the coupling terms as simple as possible without any loss of the effect of the elastic deformation on the rigid body motion and gives the uniform description in each modal coordinate.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

Computation of Nonlinear Response of Hydraulically Actuated Structures

1997 ◽  
Author(s):  
T. D. Burton ◽  
C. P. Baker ◽  
J. Y. Lew
Keyword(s):  
Rigid Body ◽  
Flexible Structures ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Beam ◽  
Test Bed ◽  
Ode Models ◽  
Hydraulically Actuated ◽  
Pressure Dynamics ◽  
Low Order

Abstract The maneuvering and motion control of large flexible structures are often performed hydraulically. The pressure dynamics of the hydraulic subsystem and the rigid body and vibrational dynamics of the structure are fully coupled. The hydraulic subsystem pressure dynamics are strongly nonlinear, with the servovalve opening x(t) providing a parametric excitation. The rigid body and/or flexible body motions may be nonlinear as well. In order to obtain accurate ODE models of the pressure dynamics, hydraulic fluid compressibility must generally be taken into account, and this results in system ODE models which can be very stiff (even if a low order Galerkin-vibration model is used). In addition, the dependence of the pressure derivatives on the square root of pressure results in a “faster than exponential” behavior as certain limiting pressure values are approached, and this may cause further problems in the numerics, including instability. The purpose of this paper is to present an efficient strategy for numerical simulation of the response of this type of system. The main results are the following: 1) If the system has no rigid body modes and is thus “self-centered,” that is, there exists an inherent stiffening effect which tends to push the motion to a stable static equilibrium, then linearized models of the pressure dynamics work well, even for relatively large pressure excursions. This result, enabling linear system theory to be used, appears of value for design and optimization work; 2) If the system possesses a rigid body mode and is thus “non-centered,” i.e., there is no stiffness element restraining rigid body motion, then typically linearization does not work. We have, however discovered an artifice which can be introduced into the ODE model to alleviate the stiffness/instability problems; 3) in some situations an incompressible model can be used effectively to simulate quasi-steady pressure fluctuations (with care!). In addition to the aforementioned simulation aspects, we will present comparisons of the theoretical behavior with experimental histories of pressures, rigid body motion, and vibrational motion measured for the Battelle dynamics/controls test bed system: a hydraulically actuated system consisting of a long flexible beam with end mass, mounted on a hub which is rotated hydraulically. The low order ODE models predict most aspects of behavior accurately.

Structures of the Phosphazenes [ClC(NPCl3)2]+PCl6 − and [CH3C(NPCl3)2]+SbCl6 − at 90 K

1997 ◽  
Vol 53 (6) ◽  
pp. 953-960 ◽  
Author(s):  
F. Belaj
Keyword(s):  
Rigid Body ◽  
Motion Analysis ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Torsion Angles ◽  
Ionic Compounds ◽  
Intramolecular Motions

The asymmetric units of both ionic compounds [N-(chloroformimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachlorophosphate, [ClC(NPCl3)2]+PCl^{-}_{6} (1), and [N-(acetimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachloroantimonate, [CH3C(NPCl3)2]+SbCl^{-}_{6} (2), contain two formula units with the atoms located on general positions. All the cations show cis–trans conformations with respect to their X—C—N—P torsion angles [X = Cl for (1), C for (2)], but quite different conformations with respect to their C—N—P—Cl torsion angles. Therefore, the two NPCl3 groups of a cation are inequivalent, even though they are equivalent in solution. The very flexible C—N—P angles ranging from 120.6 (3) to 140.9 (3)° can be attributed to the intramolecular Cl...Cl and Cl...N contacts. A widening of the C—N—P angles correlates with a shortening of the P—N distances. The rigid-body motion analysis shows that the non-rigid intramolecular motions in the cations cannot be explained by allowance for intramolecular torsion of the three rigid subunits about specific bonds.

Sign in / Sign up

Export Citation Format

Share Document