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.

Reduced Weight Design of a Flexible Rotor with Ball Bearing Stiffness Characteristics Varying with Rotational Speed and Load

2000 ◽  
Vol 122 (3) ◽  
pp. 203-208 ◽  
Author(s):  
Dong-Soo Lee ◽  
Dong-Hoon Choi
Keyword(s):  
Dynamic Behavior ◽  
Rotational Speed ◽  
High Speed ◽  
Optimization Technique ◽  
System Dynamic ◽  
Design Approach ◽  
Ball Bearings ◽  
Flexible Rotor ◽  
Augmented Lagrange Multiplier ◽  
Stiffness Characteristics

This paper presents an effective design approach for reducing the weight of a flexible rotor in ball bearings with rotational speed and load dependent stiffness characteristics under constraints on the system eigenvalues and bearing fatigue life. Design variables are chosen to be the inner radii of shaft elements, the positions of ball bearings, and the preloads on the bearings. The stiffness characteristics of high speed ball bearings are completely described as functions of applied loads and spin speed, and applied to the dynamic behavior analysis of a rotor-bearing system. A transfer matrix method is used to obtain eigenvalues of the system and an augmented Lagrange multiplier (ALM) method is employed as an optimization technique. A multi-stepped rotor supported by two angular contact ball bearings is analyzed and designed to show the speed and load dependent stiffness effect on the system dynamic behavior and to demonstrate the effectiveness of the proposed optimum design approach. The results show that the effect of the stiffness on the system dynamic behavior is noticeable and that the suggested design approach is effective. [S0739-3717(00)00803-5]

Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Shengye Lin ◽  
Shuyun Jiang
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Fixed Position ◽  
Angular Contact Ball Bearing ◽  
Face To Face ◽  
Radial Stiffness ◽  
Proposed Model ◽  
Stiffness Characteristics

This paper studies the stiffness characteristics of preloaded duplex angular contact ball bearings. First, a five degrees-of-freedom (5DOF) quasi-static model of the preloaded duplex angular contact ball bearing is established based on the Jones bearing model. Three bearing configurations (face-to-face, back-to-back, and tandem arrangements) and two preload mechanisms (constant pressure preload and fixed position preload) are included in the proposed model. Subsequently, the five-dimensional stiffness matrix of the preloaded duplex angular contact ball bearing is derived analytically. Then, an experimental setup is developed to measure the radial stiffness and the angular stiffness of duplex angular contact ball bearings. The simulated results match well with those from experiments, which prove the validity of the proposed model. Finally, the effects of bearing configuration, preload mechanism, and unloaded contact angle on the angular stiffness and the cross-coupling are studied systematically.

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mohammad Miraskari ◽  
Farzad Hemmati ◽  
Mohamed S. Gadala
Keyword(s):  
Journal Bearing ◽  
Nonlinear Coefficient ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Dynamic Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Derivatives Of ◽  
Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

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.

Nonlinear Dynamic Behavior of a Rotor Bearing System With Nonlinear Viscous Damping Suspension

2017 ◽  
Author(s):  
Shuai Yan ◽  
Bin Lin ◽  
Jixiong Fei ◽  
Pengfei Liu
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Vibration Isolation ◽  
Lubricating Oil ◽  
Viscous Damping ◽  
Oil Viscosity ◽  
Speed Range ◽  
Rotor Bearing ◽  
Nonlinear Dynamic Behavior ◽  
Bearing System

Nonlinear damping suspension has gained attention owing to its excellent vibration isolation performance. In this paper, a cubic nonlinear viscous damping suspension was introduced to a rotor bearing system for vibration isolation between the bearing and environment. The nonlinear dynamic response of the rotor bearing system was investigated thoroughly. First, the nonlinear oil film force was solved based short bearing approximation and half Sommerfeld boundary condition. Then the motion equations of the system was built considering the cubic nonlinear viscous damping. A computational method was used to solve the equations of motion, and the bifurcation diagrams were used to display the motions. The influences of rotor-bearing system parameters were discussed from the results of numerical calculation, including the eccentricity, mass, stiffness, damping and lubricating oil viscosity. The results showed that: (1) medium eccentricity shows a wider stable speed range; (2) rotor damping has little effect to the stability of the system; (3) lower mass ratio produces a stable response; (4) medium suspension/journal stiffness ratio contributes to a wider stable speed range; (5) a higher viscosity shows a wider stable speed range than lower viscosity. From the above results, the rotor bearing system shows complex nonlinear dynamic behavior with nonlinear viscous damping. These results will be helpful to carrying out the optimal design of the rotor bearing system.

scholarly journals Optimum Weight Design of a Rotor Bearing System With Dynamic Behavior Constraints

1989 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jon Li Hwang
Keyword(s):  
Dynamic Behavior ◽  
Optimization Technique ◽  
Penalty Function Method ◽  
Efficient Design ◽  
Cross Sectional ◽  
Design Algorithm ◽  
Optimum Weight ◽  
Rotor Bearing ◽  
Weight Design ◽  
Bearing System

An efficient design algorithm for optimum weight design of a rotor bearing system with dynamic behavior constraints is investigated. The constraints include the restrictions on stresses, unbalance response, and/or critical speeds. The system dynamic behaviors are analyzed by the finite element method. And the exterior penalty function method is used as the optimization technique to minimize the system weight. The system design variables are the cross-sectional areas of the shaft and the stiffnesses of the bearings. The sensitivity analysis of the system parameters is also investigated. The example of a single spool rotor bearing system is employeed to demonstrate the merits of the design algorithm with different combination of dynamic behavior constraints. At the optimum stage, it is shown that the weight of rotor system can be significantly reduced. Moreover, the optimum design weights are quite difference for various combinations of dynamic behavior constraints.

Nonlinear Vibration Prediction of a Highly Flexible Rotor Supported by an Axial Groove Journal Bearing Considering Journal Angular Whirling Motion

2019 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Ball Bearing ◽  
Journal Bearing ◽  
Flexible Rotor ◽  
Large Disk ◽  
Subcritical Bifurcation ◽  
Whirling Motion ◽  
Vibration Prediction ◽  
Rotor Bearing ◽  
Bearing System

Abstract In this study, the difference in dynamic behavior of the rotor-bearing system supported by the bearing model that considers both lateral and angular whirling motions of the journal (model A), and the model that considers only lateral whirling motion (model B) is investigated. The rotor model consists of a slender shaft, a large disk and two small disks supported by a self-aligning ball bearing and an axial groove journal bearing of L/D = 0.6. Three positions of the large disk: 410, 560, and 650 mm measured from the ball bearing, are investigated. Numerical integration of the rotor-bearing system which is modally reduced to the 1st forward mode is performed at above the onset speed of instability until either a steady state journal orbit or contact between the journal and the bearing occurs to identify the bifurcation type. Numerical results using model A indicate subcritical bifurcation with the contact between the journal and the inboard side of the bearing in all three large disk positions, whereas those of model B indicate subcritical bifurcation when the large disk position is at 410 mm, and supercritical bifurcation is observed in the other two cases. Lastly, the experiments at the same three large disk positions are performed. Subcritical bifurcation with the contact between the journal and the inboard side of the bearing is observed in all large disk positions, which conforms with the calculation result of model A. As a result, model A is essential in nonlinear vibration analysis of a highly flexible rotor system.

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