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Research Papers: Applications

An Explicit Finite-Element Model to Investigate the Effects of Elastomeric Bushing on Bearing Dynamics

[+] Author and Article Information
Lijun Cao

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: cao11@purdue.edu

Farshid Sadeghi

Cummins Distinguished Professor
of Mechanical Engineering
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: sadeghi@purdue.edu

Lars-Erik Stacke

SKF Engineering and Research Centre GPD, RKs-2,
Göteborg S-415 50, Sweden
e-mail: Lars-Erik.Stacke@skf.com

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received September 22, 2015; final manuscript received December 14, 2015; published online April 27, 2016. Assoc. Editor: Mihai Arghir.

J. Tribol 138(3), 031104 (Apr 27, 2016) (13 pages) Paper No: TRIB-15-1342; doi: 10.1115/1.4032526 History: Received September 22, 2015; Revised December 14, 2015

This work presents a numerical simulation which studies the effect of elastomeric bushing on the dynamics of a deep-groove ball bearing. To achieve the objective, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model a cylindrical elastomeric bushing, which was then coupled with an existing dynamic bearing model (DBM). Constitutive relationship for the elastomer is based on the Arruda–Boyce model combined with a generalized Maxwell-element model to capture both hyperelastic and viscoelastic behaviors of the material. Comparisons between the bushing model developed for this investigation and the existing experimental elastomeric bushing study showed that the results are in good agreement. Parametric studies were conducted to show the effects of various elastomeric material properties on bushing behavior. It was also shown that a desired bushing support performance can be achieved by varying bushing geometry. Simulations using the combined EFEM bushing and DBM model demonstrated that the elastomeric bushing provides better compliance to bearing misalignment as compared to a commonly used rigid support model. As a result, less ball slip and spin are generated. Modeling with a bearing surface dent showed that vibrations due to surface abnormalities can be significantly reduced using elastomeric bushing support. It has also been shown that choosing a proper bushing is an efficient way to tuning bushing vibration frequencies.

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Figures

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Fig. 1

Flowchart of the combined bearing bushing model

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Fig. 2

Elastomer material rheological model

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Fig. 3

Deformation history of radial step loads with various ramp speeds

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Fig. 4

FE mesh for the same elastomer bushing used by Kadlowec et al. [18]

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Fig. 5

Radial force relaxation response obtained by Kadlowec et al. [18]

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Fig. 6

Radial force relaxation response obtained using the combined model

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Fig. 7

Effect of excitation frequency on the hysteresis response with 1 mm harmonic displacement amplitude

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Fig. 8

Elastomer bushing excitation deformation with various maximum displacements (1 Hz harmonic deformation)

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Fig. 9

Time history of step deformation load

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Fig. 10

Elastomer bushing nonlinear response at large deformation for various excitation speeds on top of a relaxed state curve

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Fig. 11

Harmonic excitation with varying material properties—1 mm excitation at 0.1 Hz

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Fig. 12

Harmonic excitation with varying material properties—1 mm excitation at 10 Hz

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Fig. 13

Cylindrical bushing dimensions

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Fig. 14

Dimensionless dynamic stiffness as a function of dimensionless length

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Fig. 15

Hysteresis damping ratio as a function of dimensionless length

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Fig. 16

Dimension less dynamic stiffness as a function of dimensionless inner diameter

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Fig. 17

Hysteresis damping ratio as a function of dimensionless diameter

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Fig. 18

Bulging of end planes of short and long bushings

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Fig. 19

Impact load time history—500 N maximum amplitude

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Fig. 20

Reaction force on OR after impact for different thicknesses

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Fig. 21

Reaction force on OR after impact for different material modules

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Fig. 22

Steady-state IR center of mass motions in rotating unbalance (bushing thickness: 10 mm, 20 mm and 30 mm)

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Fig. 23

Location of dent created at the bottom of bearing outer race

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Fig. 24

Normal contact force between ball and outer race in a bearing (fixed outer race) with dent at bottom (270 deg)

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Fig. 25

Normal contact force between ball and outer race in a bearing (outer race supported by elastomer bushing) with dent at bottom (270 deg)

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Fig. 26

Inner race motion in Z-direction in the bearing (fixed outer race) with dent (along Z-direction)

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Fig. 27

Inner race motion in Z-direction in the bearing (outer race supported by elastomer bushing) with dent (along Z-direction)

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Fig. 28

FFT analysis on the IR motions plotted in Figs. 26 and 27

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Fig. 29

Effect of material modulus (CR) on normal contact force between ball and outer race in a bearing with dent at 270 deg

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Fig. 30

Effect of viscoelastic constant (γj0) on normal contact force between ball and outer race in a bearing with dent at 270 deg

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Fig. 31

Angular misalignment test—normal contact force between ball and outer race (outside curve: fixed outer race and inside curve: outer race supported by elastomer bushing)

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Fig. 32

Angular misalignment test—slip magnitude between ball and outer race

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Fig. 33

Angular misalignment test—ball spin at contact point

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Fig. 34

Comparison of moment–angle curve between bearings with fixed outer race and bushing supported outer race

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