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Research Papers

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

[+] Author and Article Information
C. K. Babu, N. Tandon

 Industrial Tribology, Machine Dynamics and Maintenance Engineering Centre (ITMMEC), IIT Delhi, New Delhi-110 016, India

R. K. Pandey1

 Industrial Tribology, Machine Dynamics and Maintenance Engineering Centre (ITMMEC), IIT Delhi, New Delhi-110 016, Indiarajpandey@mech.iitd.ac.in

1

Corresponding author. Present address: Associate Professor, Department of Mechanical Engineering, IIT Delhi, New Delhi-110016, India.

J. Vib. Acoust 134(1), 011006 (Dec 22, 2011) (12 pages) doi:10.1115/1.4005140 History: Received April 26, 2010; Revised September 07, 2011; Published December 22, 2011; Online December 22, 2011

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of rigid rotor supported on two angular contact ball bearings

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Figure 2

Schematic diagram of waviness model

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Figure 3

Flow chart for numerical computation

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Figure 4

Test rig for experimentation

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Figure 5

Comparison of ideal profile of outer race with waviness machined profile

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Figure 6

(a) X-direction vibration of left side bearing achieved through experimentation [F = 50 N, shaft’s rotational speed = 1500 rpm, WA = 30 μm, WO = 7]. (b) Enlarged view of encircled experimental vibration in (a) [F = 50 N, shaft’s rotational speed = 1500 rpm, WA = 30  μm, WO = 7]. (c) X-direction vibration of left side bearing achieved from proposed theoretical model [F = 50 N, shaft’s rotational speed = 1500 rpm, WA = 30 μm, WO = 7].

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Figure 7

(a) X-direction vibration of rotor CG without waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm]. (b) Y-direction vibration of rotor CG without waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm].

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Figure 8

(a) X-direction vibration of rotor CG without waviness [F = 100 N, Pr  = 100 N, shaft’s rotational speed = 2500 rpm]. (b) Y-direction vibration of rotor CG without waviness [F = 100 N, Pr  = 100 N, shaft’s rotational speed = 2500 rpm].

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Figure 9

(a) X-direction vibration of rotor CG in presence of inner race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm]. (b) X-direction vibration of rotor CG in presence of inner race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm].

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Figure 10

(a) Y-direction vibration of rotor CG in presence of inner race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm]. (b) Y-direction vibration of rotor CG in presence of inner race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm].

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Figure 11

(a) Z-direction vibration of rotor CG in presence of inner race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm]. (b) Z-direction vibration of rotor CG in presence of inner race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm].

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Figure 12

(a) X-direction vibration of rotor CG in presence of outer race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm]. (b) X-direction vibration of rotor CG in presence of outer race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm].

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Figure 13

(a) Y-direction vibration of rotor CG in presence of outer race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm]. (b) Y-direction vibration of rotor CG in presence of outer race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm].

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Figure 14

(a) Z-direction vibration of rotor CG in presence of outer race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm]. (b) Z-direction vibration of rotor CG in presence of outer race radial waviness [F = 50 N, Pr  = 100 N, shaft’s rotational speed = 1500 rpm].

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