Nonlinear Dynamic Analysis of an Unsymmetrical Generator-Bearing System

2007 ◽  
Vol 129 (4) ◽  
pp. 448-457 ◽  
Author(s):  
Zhansheng Liu ◽  
Senlin Huang ◽  
Jiexian Su
Keyword(s):  
Dynamic Behavior ◽  
Degrees Of Freedom ◽  
Synthesis Method ◽  
Nonlinear Dynamic Analysis ◽  
Three Dimension ◽  
Dynamic Effects ◽  
Order Model ◽  
Rotor Stiffness ◽  
Rotating Coordinates ◽  
Bearing System

Considering both nonlinear oil film force and unsymmetrical stiffness, this paper presents a mechanical model of a generator-bearing system. The complex mode synthesis method is used to reduce the linear degrees of freedom of the high order model in the rotating coordinates, and one-order modal differential equations are obtained which may not be solved directly by Newmark-β method. To solve this problem, a modified Newmark-β method is presented to investigate dynamic effects of the asymmetry of rotor stiffness, the viscosity of oil, the rotor unbalance and the ratio of length to diameter of bearings. Three-dimension diagrams and unfiltered vibration curves are used as tools to examine the dynamic behavior of the system, and some insights into the dynamic behavior are given. Numerical results show that instability of the system may be improved by modifying these parameters.

Nonlinear Dynamic Analysis of Cantilever Beam Using POD Based Reduced Order Model

2015 ◽  
Vol 786 ◽  
pp. 398-403 ◽  
Author(s):  
Kulkarni Atul Shankar ◽  
Manoj Pandey
Keyword(s):  
Dynamic Analysis ◽  
Large Deformation ◽  
Cantilever Beam ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Numerical Technique ◽  
Nonlinear Dynamic Analysis ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order

In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

Chaos and Nonlinear Dynamic Analysis of Porous Air Bearing System

2015 ◽  
Vol 764-765 ◽  
pp. 204-207
Author(s):  
Cheng Chi Wang ◽  
Jui Pin Hung
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Effective Means ◽  
Nonlinear Dynamic Analysis ◽  
Transformation Method ◽  
Dynamic Responses ◽  
Air Bearing ◽  
Dynamic Behaviors ◽  
Rotor Mass ◽  
Bearing System

The chaos and nonlinear dynamic behaviors of porous air bearing system are studied by a hybrid numerical method combining the finite difference method (FDM) and differential transformation method (DTM). The numerical results are verified by two different schemes including hybrid method and FDM and the current analytical results are found to be in good agreement. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass is increased. From the dynamic responses of the rotor center, they reveal complex dynamic behaviors including periodic, sub-harmonic motion and chaos. The results of this study provide an understanding of the nonlinear dynamic behavior of PAB systems characterized by different rotor masses. Specifically, the results have shown that system exists chaotic motion over the ranges of rotor mass 10.66≤Mr<13.7kg. The proposed method and results provide an effective means of gaining insights into the porous air bearing systems.

scholarly journals A Dynamic Analysis of a Flexible Rotor in Ball Bearings with Nonlinear Stiffness Characteristics

1997 ◽  
Vol 3 (2) ◽  
pp. 73-80 ◽  
Author(s):  
Dong-Soo Lee ◽  
Dong-Hoon Choi
Keyword(s):  
Dynamic Behavior ◽  
Degrees Of Freedom ◽  
Analysis Approach ◽  
Nonlinear Stiffness ◽  
Ball Bearings ◽  
Flexible Rotor ◽  
Combined Loads ◽  
Rotor Bearing ◽  
Stiffness Characteristics ◽  
Bearing System

This paper presents an effective analysis approach for a flexible rotor in ball bearings with nonlinear stiffness characteristics to obtain realistic dynamic behavior results. The ball bearing is modeled in five degrees of freedom and the nonlinear stiffness characteristics of the bearing are completely described as functions of combined loads and spin speed. For dynamic behavior analysis of the nonlinear rotor-bearing system, a transfer-matrix method is iteratively used until the bearing displacements and the shaft displacements at every bearing location converge to the same values. The results show that the nonlinear stiffness characteristics of ball bearings significantly influence system dynamic behaviors and the proposed analysis approach for the nonlinear rotor-bearing system is effective.

Optimization of the dynamic behavior of vehicle structures by means of passive interface controls

2016 ◽  
Vol 24 (3) ◽  
pp. 466-491 ◽  
Author(s):  
Xingrong Huang ◽  
Louis Jézéquel ◽  
Sébastien Besset ◽  
Lin Li
Keyword(s):  
Dynamic Behavior ◽  
Degrees Of Freedom ◽  
Passive Control ◽  
Dynamic Performance ◽  
Synthesis Method ◽  
Optimal Solution ◽  
Kriging Interpolation ◽  
Objective Functions ◽  
Modal Synthesis ◽  
Acoustic Comfort

As a form of passive control, padding rubber layers onto the most heavily deformed zones of a system can improve the dynamic behavior and the acoustic comfort of a vehicle system. This paper proposes an extensive hybrid modal synthesis method in order to study coupled fluid-structure systems, in retaining a few degrees of freedom. Modal criteria, corresponding to noise transmission paths between substructures in the system, have been derived to characterize the dynamic phenomenon from a modal view. These criteria were then substituted by Kriging interpolation models to avoid prohibitive simulation steps during optimization of the complex system. Once the mathematical models of the investigated modal criteria were established and the multi-objective functions for rubber characteristics defined, an approximate optimal solution leading to superior dynamic performance could be obtained based on a genetic algorithm. The analytical results and numerical experiments conducted have also justified the efficiency of our proposed strategy.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

Modal synthesis method of lateral vibration analysis for rotor-bearing system

2002 ◽  
Vol 80 (32) ◽  
pp. 2537-2549 ◽  
Author(s):  
Chun-Ping Zou ◽  
Hong-Xing Hua ◽  
Duan-Shi Chen
Keyword(s):  
Vibration Analysis ◽  
Synthesis Method ◽  
Lateral Vibration ◽  
Modal Synthesis ◽  
Rotor Bearing ◽  
Bearing System

Dynamic Behavior Analysis of Three-Span Rotor-Bearing System with Rub-Impact Fault

2012 ◽  
Vol 460 ◽  
pp. 160-164 ◽  
Author(s):  
Song He Zhang ◽  
Yue Gang Luo ◽  
Bin Wu ◽  
Bang Chun Wen
Keyword(s):  
Nonlinear Dynamics ◽  
Behavior Analysis ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Rotor System ◽  
System Response ◽  
Rotor Bearing ◽  
Set Up ◽  
Bearing System ◽  
Main Influence

The dynamic model of the three-span rotor-bearing system with rub-impact fault was set up. The influence to nonlinear dynamics behaviors of the rotor-bearing system that induced by rub-impact of one disc, two discs and three discs were numerically studied. The main influence of the rotor system response by the rub-impact faults are in the supercritical rotate speed. There are mutations of amplitudes in the responses of second and third spans in supercritical rotate speed when rub-impact with one disc, and there are chaotic windows in the response of first span, and jumping changes in second and third spans when rub-impact with two or three discs.

Design of Workspace of Human Fingers and Computer Keyboard Operation

2014 ◽  
Vol 484-485 ◽  
pp. 1118-1125
Author(s):  
Rao Shun
Keyword(s):  
Degrees Of Freedom ◽  
Index Finger ◽  
Operation Mode ◽  
Penalty Function Method ◽  
Three Dimension ◽  
Mechanism Model ◽  
Reachable Workspace ◽  
Human Arm ◽  
Dimension Space ◽  
Human Finger

There are more and more complex tools and machinery that need be operated by human fingers in our modem industrial environment. Such as computer keyboards, screwdriver, handle wrench, button and switch. All of those should be designed to work effectively and safely with the operators for whom they were designed. At first, ergonomic consideration in design is reachable; this means the operators fingertip must be able to reach the operating component. This is generally no question because human arm has much more degrees of freedom required to position his arms, hands and fingers in the three-dimension space. However, some times we need the finger operate with a fixed wrist. For example in the case in the typing, the reachable workspace of the finger must take into account in such situation.Finger contacting is the most familiar operation mode of the man-machine system, and the index finger takes on the primary operation tasks. From viewpoint of ergonomic engineering, the operation component should be placed within the workspace of the fingertip to reduced or eliminate the movement of palm and arm should to the greatest extent during finger manipulation. Therefore the research of the workspace of ginger is significant to the ergonomic design of the operation device. In this paper, the reachable workspace and workspace under direction restrain of contacting for the index finger are determined using serial mechanism model and the Penalty Function Method based on geometric measurement of human body. The optimal operating position and orientation of human finger is analyzed.

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