Nonlinear Vibration Analysis of an Elastic Rotor Supported on Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
C. K. Babu ◽  
N. Tandon ◽  
R. K. Pandey
Keyword(s):  
Nonlinear Vibration ◽  
Elastic Deformation ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Ball Bearings ◽  
Rigid Rotor ◽  
Six Degrees Of Freedom ◽  
Extension Work ◽  
Inner Race ◽  
Rotor Model

Nonlinear vibration analysis of an elastically deformable shaft supported on two lubricated angular contact ball bearings is reported herein considering six-degrees of freedom (6-DOF) and waviness on races and balls. This is an extension work of the investigation published by the authors Babu, C. K., Tandon, N., and Pandey, R. K., 2012, “Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degree of Freedom and Waviness on Balls and Races,” ASME J. Vib. Acoust., 134, p. 011006. Elastic deformation of shaft, frictional moment, and waviness on races and balls have been incorporated in the model for the vibration investigations of rotor's CG. Two noded 3D Timoshenko beam element having 6-DOF has been employed in the computation of the shaft's deformation. Governing equations with appropriate boundary conditions have been solved using 4th order Runge–Kutta method. It is observed that vibration amplitude enhances considerably after incorporating the elastic deformation in comparison to the amplitude achieved using rigid rotor model approach. Moreover, the influence of outer race's radial waviness is large on the amplitudes of vibrations in comparison to radial waviness of inner race. However, it is worth noting here that in case of rigid rotor model the presence of radial waviness on inner race yields high amplitudes of vibrations.

Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
C. K. Babu ◽  
N. Tandon ◽  
R. K. Pandey
Keyword(s):  
Degrees Of Freedom ◽  
High Amplitude ◽  
Ball Bearings ◽  
Rigid Rotor ◽  
Outer Race ◽  
Six Degrees Of Freedom ◽  
Proposed Model ◽  
Sinusoidal Functions ◽  
Rotor Bearings ◽  
Inner Race

Nonlinear vibration analysis of angular contact ball bearings supporting a rigid rotor is presented herein considering the frictional moments (load dependent and load independent components of frictional moments) in the bearings. Six degrees of freedom (DOF) of rigid rotor is considered in the dynamic modeling of the rotor-bearings system. Moreover, waviness on surfaces of inner race, outer race, and ball are considered in the model by representing it as sinusoidal functions with waviness orders of 6, 15, and 25. Two amplitudes of waviness, 0.05 and 0.2 μm, are considered in the investigation looking for the practical aspects. The proposed model is validated with the experimental results by performing the experiments. Moreover, the present model has also been validated with published results of researchers by incorporating needful changes in the DOF in the proposed model. Based on the computed results, it is observed that load dependent frictional moment (LDFM) significantly enhances the amplitudes of vibrations in comparison to load independent frictional moment (LIFM) irrespective to values of waviness amplitude and waviness order. The influence of inner race waviness is relatively more on the vibrations in comparison to waviness of outer race and ball. Moreover, vibrations of system enhance considerably at high amplitude of waviness, increase in the order of waviness, and at elevated operating parameters.

Vibration Analysis of Rotor With Transverse Surface Cracks

2003 ◽  
Author(s):  
Dan Guo ◽  
Fu-Lei Chu ◽  
Yong-Yong He
Keyword(s):  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Surface Cracks ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Six Degrees Of Freedom ◽  
Flexibility Matrix ◽  
Vibration Responses

The vibration of cracked rotor is investigated by numerical method. The FEM is used to model the rotor with cracks. Six degrees of freedom are considered in each elemental node. Full 6×6 flexibility matrix is deduced by Papadopoulos and Dimarogonas’ method, and 12×12 stiffness matrix of cracked element is derived. The influence of one or more cracks on the natural frequencies and different modals (including bending modal, torsion modal and longitudinal modal) of cracked rotor is explored. Vibration responses of rotor with open cracks or breathing crack loading by eccentric force and rotor gravity force are obtained and analyzed by numerical integer method and spectral technology. The coupling of lateral, longitudinal and torsion vibrations due to transverse surface crack is studied. It is concluded that the above research is useful in detecting crack in rotor.

Nonlinear Excitation Model of Ball Bearing Waviness in a Rigid Rotor Supported by Two or More Ball Bearings Considering Five Degrees of Freedom

2001 ◽  
Vol 124 (1) ◽  
pp. 82-90 ◽  
Author(s):  
G. H. Jang ◽  
S. W. Jeong
Keyword(s):  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Angular Displacement ◽  
Equations Of Motion ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rigid Rotor ◽  
Nonlinear Load ◽  
Rolling Elements ◽  
Nonlinear Equations Of Motion

This research presents a nonlinear model to analyze the ball bearing vibration due to the waviness in a rigid rotor supported by two or more ball bearings. The waviness of a ball and each races is modeled by the superposition of sinusoidal function, and the position vectors of inner and outer groove radius center are defined with respect to the mass center of the rotor in order to consider five degrees of freedom of a general rotor-bearing system. The waviness of a ball bearing is introduced to these position vectors to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. Numerical results of this research are validated with those of prior researchers. The proposed model can calculate the translational displacement as well as the angular displacement of the rotor supported by two or more ball bearings with waviness. It also characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing, and the sideband frequencies resulting from nonlinearity of the waviness interaction.

Control of processing at multi-tool two-support setup

2020 ◽  
pp. 67-73
Author(s):  
N.D. YUsubov ◽  
G.M. Abbasova
Keyword(s):  
Degrees Of Freedom ◽  
Factor Model ◽  
Angular Displacement ◽  
Factor Models ◽  
Technological System ◽  
Displacement Control ◽  
Model Accuracy ◽  
Six Degrees Of Freedom ◽  
Angular Displacements ◽  
And Control

The accuracy of two-tool machining on automatic lathes is analyzed. Full-factor models of distortions and scattering fields of the performed dimensions, taking into account the flexibility of the technological system on six degrees of freedom, i. e. angular displacements in the technological system, were used in the research. Possibilities of design and control of two-tool adjustment are considered. Keywords turning processing, cutting mode, two-tool setup, full-factor model, accuracy, angular displacement, control, calculation [email protected]

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