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.

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.

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.

The Effect of Waviness on Vibrations Associated Witli Ball Bearings

1999 ◽  
Vol 121 (4) ◽  
pp. 667-677 ◽  
Author(s):  
Nizami Aktu¨rk
Keyword(s):  
Computer Program ◽  
Ball Bearings ◽  
Surface Waviness ◽  
Outer Race ◽  
Rolling Surface ◽  
Frequency Domains ◽  
Axial Vibrations ◽  
Experimental Researches ◽  
Inner Race ◽  
Time And Frequency Domains

In this paper, the radial and axial vibrations of a rigid shaft supported by a pair of angular contact ball bearings is studied. The effect of bearing running surface waviness on the vibration of the shaft is investigated. A computer program was developed to simulate inner race, outer race, and rolling surface waviness with the results presented in time and frequency domains. Results obtained from the similation programme are quantatively in good aggrement with various authors’ experimental researches.

scholarly journals Investigation of Factors Influencing the Structural Vibration in Ball Bearings

2000 ◽  
Vol 6 (5) ◽  
pp. 321-331 ◽  
Author(s):  
Kapil Mehra ◽  
Kambiz Farhang ◽  
Jayanta Datta
Keyword(s):  
High Speed ◽  
Structural Vibration ◽  
Ball Bearings ◽  
Appreciable Change ◽  
Outer Race ◽  
Nonlinear Springs ◽  
Lumped Parameter ◽  
Intermittent Contact ◽  
Parameter Approach ◽  
Inner Race

Hertzian equation for elastic contact is utilized along with lumped parameter approach to obtain the equations that govern the structural vibration of ball bearings. The lumped parameter formulation is obtained by treating various elements with mass lumped at their centers of gravity and the contact as nonlinear springs with nonlinear spring rates.Effects of preload, ball rotational speed, and damping are studied using the formulation. It is found that in the presence of preload, irrespective of the load magnitude, contact is maintained with both the inner and the outer races. Hence, responses obtained with and without the check for ball/inner race and ball/outer race interferences are identical. In addition, no appreciable change is observed in the responses when the preload value is varied from 1 to 10 N. At high speed of operation, the balls are found to maintain contact with the outer ring, whereas intermittent contact with the inner ring occurs for brief periods of time. Introduction of lubricant is found to dampen the oscillations considerably.

A Dynamic Analysis of Cage Instability in Ball Bearings

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Takashi Nogi ◽  
Kazuaki Maniwa ◽  
Noriko Matsuoka
Keyword(s):  
Friction Coefficient ◽  
Dynamic Analysis ◽  
High Speed ◽  
Contact Stiffness ◽  
Ball Bearings ◽  
Analysis Program ◽  
Outer Race ◽  
Group Speed ◽  
Rotational Direction ◽  
Inner Race

Cage motions in ball bearings are investigated using a dynamic analysis program. Increases in the cage friction coefficient induce unstable motions of the cage. The instability is more likely to occur under high load and low‐speed conditions due to less ball-race sliding. A simple theory of cage instability is developed, and a critical cage friction coefficient formula is proposed, which is a function of the cage mass, ball-race traction, ball-cage contact stiffness, cage rotational speed, and number of balls. The prediction of this formula agrees with the results of the dynamic analysis. With a nonuniform separation between the balls, a high-speed whirl is superimposed on the normal whirl with the ball group speed. The direction of the high-speed whirl is the same as the cage rotational direction in inner race rotation (IR), but they are opposite in outer race rotation (OR). These results agree with some experimental results in the literature and validate the dynamic analysis.

Investigation of Dynamic Processes in Ball Bearings with Defects

2013 ◽  
Vol 198 ◽  
pp. 651-656 ◽  
Author(s):  
Marijonas Bogdevičius ◽  
Viktor Skrickij
Keyword(s):  
Mathematical Model ◽  
Ball Bearing ◽  
Dynamic Processes ◽  
Experimental Investigations ◽  
Ball Bearings ◽  
Outer Race ◽  
Rolling Element ◽  
Inner Race

The paper considers the dynamics of ball bearings with defects. A mathematical model of a ball bearing with defects is offered. The performed theoretical and experimental investigations of ball bearings with defects are described. Five cases of various defects are investigated, including the defective outer race, the defective inner race, the defective rolling element, the defective inner and outer races, the rolling element and a separator, the worn-out ball bearing.

Marine Vessel Dynamics Using 6-DOF Simulations

2008 ◽  
Author(s):  
Craig J. Pregnalato ◽  
Kyong-Huhn Lee
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
High Amplitude ◽  
Cfd Simulations ◽  
Six Degrees Of Freedom ◽  
Interface Capturing ◽  
Surface Ship ◽  
Vessel Motion ◽  
Marine Vessels ◽  
Fully Coupled

The response of marine vessels to steady currents and unsteady wave motions is presented using six degrees-of-freedom CFD simulations. The equations governing the fluid flow are coupled with the rigid-body equations of motion to predict the response of surface ships when driven by high-amplitude waves. In addition, the maneuvering performance of a submarine is analysed for a constant heading and depth. Such fully coupled simulations allow the accurate prediction of the hydrodynamic forces acting on the vessel as well as the corresponding vessel motion and are becoming increasingly important from a design standpoint. In these simulations, a high-resolution interface-capturing scheme is used to efficiently capture the dynamics of breaking and overturning waves and to examine their impact on a surface ship. The dynamics of the vessel are investigated in detail with particular emphasis on its angular response (i.e. pitch, roll and yaw).

Numerical investigation of the oil–air distribution inside ball bearings with under-race lubrication

2021 ◽  
pp. 135065012110105
Author(s):  
Le Jiang ◽  
Yaguo Lyu ◽  
Wenjun Gao ◽  
Pengfei Zhu ◽  
Zhenxia Liu
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Volume Fraction ◽  
Volume Flow Rate ◽  
Ball Bearings ◽  
Outer Race ◽  
Rotating Speed ◽  
Oil Distribution ◽  
Hole Configuration ◽  
Inner Race

Oil distribution inside the under-race lubricated bearing is crucial for lubrication and cooling of high-speed ball bearings. An under-race lubricated ball bearing is modeled to numerically investigate the effects of operating parameters and feed hole configuration on the distribution behavior of lubricant oil. The results of the numerical simulation indicate that the average oil volume fraction changes with a convex trend as the outer race rotating speed increases, while it changes monotonically with the inner race rotating speed, oil volume flow rate, and oil temperature. The extent of oil spreading on the outer race, cage, ball, and inner race decreases successively. Optimizing the feed hole configuration according to the average oil volume fraction is helpful to achieve precise lubrication of the under-race lubricated ball bearing.

scholarly journals Parametric Study of the Lubrication of Thrust Loaded 120-MM Bore Ball Bearings to 3 Million DN

1974 ◽  
Vol 96 (3) ◽  
pp. 515-524 ◽  
Author(s):  
H. Signer ◽  
E. N. Bamberger ◽  
E. V. Zaretsky
Keyword(s):  
Parametric Study ◽  
Contact Angles ◽  
Inlet Temperature ◽  
Ball Bearings ◽  
Outer Race ◽  
Lubricant Flow ◽  
Endurance Tests ◽  
High Degree ◽  
Inner Race

A parametric study was performed with 120-mm bore angular-contact ball bearings under varying thrust loads, bearing and lubricant temperatures, and cooling and lubricant flow rates. Contact angles were nominally 20 and 24 deg with bearing speeds to 3 million DN. Endurance tests were run at 3 million DN and a temperature of 492 K (425 deg F) with 10 bearings having a nominal 24-deg contact angle at a thrust load of 22241 N (5000 lb). Bearing operating temperature, differences in temperatures between the inner and outer races, and bearing power consumption can be tuned to any desirable operating requirement by varying 4 parameters. These parameters are outer-race cooling, inner-race cooling, lubricant flow to the inner race, and oil inlet temperature. Preliminary endurance tests at 3 million DN and 492 K (425 deg F) indicate that long-term bearing operation can be achieved with a high degree of reliability.

The impact of vibration response due to rolling bearing components waviness on the performance of grinding machine spindle system

2019 ◽  
Vol 233 (3) ◽  
pp. 747-762 ◽  
Author(s):  
Mohammed Alfares ◽  
Ghanim Al-Daihani ◽  
Jasim Baroon
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Dynamical System ◽  
Vibration Response ◽  
Spindle System ◽  
Outer Race ◽  
Ball Surface ◽  
Machine Spindle ◽  
Grinding Machine ◽  
The Impact ◽  
Inner Race

In this research, an analytical model based on a five-degrees-of-freedom nonlinear dynamical system was utilized to investigate the impact of vibration response due to inner race, outer race, and ball bearing waviness on the performance of grinding machine spindle system supported by two angular ball bearings. The waviness of rolling elements is modeled as a sinusoidal function is incorporated along the inner or outer races of bearing and ball surface. The elastic deflection and nonlinear contact force are calculated based on Hertzian contact model, while the shaft has five-degrees-of-freedom motions, three translational and two angular motions. The five–degrees-of-freedom nonlinear governing equations of the spindle system were developed taking into consideration the effect of outer race, inner race, and ball surface waviness, which are included in the kinematic constraints and force equilibrium equations of a ball. The developed model and its results are validated against results found in literature. Results by this paper indicate that the inner race waviness can significantly distort the tolerance and machining quality of grinding spindle-bearing systems more than does waviness in the outer race and ball elements. This is because the inner race waviness generates more complicated vibrations than the outer race and ball waviness. The most severe vibrations caused by the inner race waviness were found to occur when the waviness was of the order that is equal to multiple of number of balls in a bearing set plus or minus one ([Formula: see text]).

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