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Research Papers: Applications

A Combined EFEM–Discrete Element Method Dynamic Model of Rotor–Bearing–Housing System

[+] 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 & Research Centre GPD,
RKs-2,
Gothenburg 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 October 21, 2016; final manuscript received March 8, 2017; published online June 30, 2017. Assoc. Editor: Mihai Arghir.

J. Tribol 139(6), 061102 (Jun 30, 2017) (10 pages) Paper No: TRIB-16-1332; doi: 10.1115/1.4036378 History: Received October 21, 2016; Revised March 08, 2017

In this paper, a model was developed to study the effects of rotor and support flexibilities on the performance of rotor–bearing–housing system. The system is composed of a flexible rotor and two supporting deep-groove ball bearings mounted in flexible bearing housings. The dynamics of the ball bearings were simulated using an existing dynamic bearing model, which was developed using the discrete element method (DEM). The explicit finite element method (EFEM) was used to model the flexibilities of the rotor and bearing support. In order to combine the dynamic bearing model with finite element rotor and support system, new contact algorithms were developed for the interactions between the various components in the system. The total Lagrangian formulation approach was applied to decrease the computational effort needed for modeling the rotor–bearing–housing system. The combined model was then used to investigate the effects of bearing clearances and housing clearances. And it was found that, as the rotor is deformed due to external loading, the clearances have a significant impact on the bearing varying compliance motion and reaction moments. Results also show that deformation of the flexible housing depends on the total force and moment generated within the bearing due to rotor deformation. The first critical speed of rotor was simulated to investigate the unbalance response of the rotor–bearing system. It was demonstrated that rotor critical speed has a significant effect on inner race displacement and reaction moment generated at bearing location.

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References

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Figures

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Fig. 1

Flowchart of combined EFEM–DEM rotor–bearing model

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Fig. 2

Overlap between two bodies in Hertzian contact

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Fig. 3

Euler angles of rotor cross section between body-fixed frame and inertial frame

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Fig. 4

The interaction between rigid and flexible bodies

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Fig. 5

(a) Initial state of combined EFEM–DEM dynamic rotor–bearing model and (b) dimensions (in meter) of pillow block bearing housing and EFEM mesh

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Fig. 6

Comparison of bearing IR varying compliance motions in Z direction between four different bearing clearance cases

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Fig. 7

Comparison of bearing IR varying compliance motions in Y direction between four different bearing clearance cases

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Fig. 8

Illustration of contact force between balls and OR under radial load

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Fig. 9

The combined rotor–bearing model with radial load applied at rotor center (von Mises stress in megapascals, as shown in the figure)

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Fig. 10

Deformed configuration of EFEM rotor (deformation × 40, von Mises stress in megapascals, as shown in the figure)

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Fig. 11

Cross-sectional view of contact forces between balls and bearing race under radial load and rotor misalignment

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Fig. 12

(a) Normal contact force between one ball and OR as the ball moves around the OR and (b) reaction moment in the bearing as a function of the tilt angle of bearing IR

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Fig. 13

Contact force distribution between bearing OR and housing for housings with various clearance

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Fig. 14

Effect of housing clearance on the IR varying compliance motions in Y direction

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Fig. 15

Cross-sectional view of bearing housing free-body diagram

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Fig. 16

Deformed configuration of EFEM rotor and housings (housing deformation × 2000)

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Fig. 17

The combined rotor–bearing model with overhung load applied at the end of the rotor (von Mises stress in megapascals, as shown in the figure)

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Fig. 18

Deformed configuration of EFEM rotor and housings under overhung load (housing deformation × 2000, von Mises stress in megapascals, as shown in the figure)

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Fig. 19

Magnitude of rotor deflection as rotor speed is increased from 0 to 10,000 rpm

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Fig. 20

Bearing IR displacement in Z for a rotor–bearing model with fixed OR and one with flexible housing support

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Fig. 21

Bearing IR displacement in Y for a rotor–bearing model with fixed OR and one with flexible housing support

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Fig. 22

Deformed configurations of EFEM rotor and housings at first critical speed (motions captured at every 90 deg of rotor rotation, and the arrows indicate the directions of rotor deformation, von Mises stress in megapascals, as shown in the figure)

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Fig. 23

Reaction moment of bearing as the rotor goes through first critical speed

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