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Research Papers: Hydrodynamic Lubrication

Profile Design for Misaligned Journal Bearings Subjected to Transient Mixed Lubrication

[+] Author and Article Information
Thomas Gu

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208
e-mail: thomasgu2014@u.northwestern.edu

Q. Jane Wang

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208
e-mail: qwang@northwestern.edu

Shangwu Xiong

SWANTEC Software and Engineering ApS,
373, Diplomvej Kongens,
2800 Kongens Lyngby, Denmark
e-mail: sx@swantec.com

Zhong Liu

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208
e-mail: zhongliu2018@u.northwestern.edu

Arup Gangopadhyay

Ford Motor Company,
Research and Advanced Engineering,
Dearborn, MI 48121
e-mail: agangopa@ford.com

Zhiqiang Liu

Ford Motor Company,
Research and Advanced Engineering,
Dearborn, MI 48121
e-mail: zliu10@ford.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received November 8, 2018; final manuscript received April 4, 2019; published online May 9, 2019. Assoc. Editor: Stephen Boedo.

J. Tribol 141(7), 071701 (May 09, 2019) (15 pages) Paper No: TRIB-18-1470; doi: 10.1115/1.4043506 History: Received November 08, 2018; Accepted April 04, 2019

Misalignment between the shaft and the bearing of a journal bearing set may be inevitable and can negatively impact journal bearing performance metrics in many industrial applications. This work proposes a convex profile design of the journal surface to help counteract the negative effects caused by such a misalignment. A transient mass-conserving hydrodynamic Reynolds equation model with the Patir–Cheng flow factors and the Greenwood–Tripp pressure–gap relationship is developed to conduct the design and analysis. The results reveal that under transient impulse loading, a properly designed journal profile can help enhance the minimum film thickness, reduce mean and peak bearing frictions, and increase bearing durability by reducing the asperity-related wear load. The mechanism for the minimum film thickness improvement due to the profile design is traced to the more even distribution of the hydrodynamic pressure toward the axial center of the bearing. The reason for the reductions of the friction and wear load is identified to be the decreased asperity contact by changing the lubrication regime from mixed lubrication to nearly hydrodynamic lubrication. Parametric studies and a case study are reported to highlight the key points of the profile design and recommendations for profile height selection are made according to misalignment parameters.

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Figures

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Fig. 1

Journal bearing schematic is not drawn to scale; the clearance and profile are exaggerated for clarity. (a) Cross-sectional view of the eccentric and misaligned journal. O1: the bearing geometric center, O2: the location of the half-length (y = L/2) eccentricity coordinates, O3 and O4: the journal centers at the rear (y = 0) and front ends (y = L), respectively. e0: the half-length eccentricity with e0X and e0Y for the eccentricity components. ϕ0: the load angle. ψ: the angle between journal rear center (line O3O4) and the eccentricity vector (line O1O2). θmin: the circumferential angular location of the tip of the eccentricity vector. (b) Misaligned journal bearing with length, L, containing a journal axial profile with misalignment angle, β, defined between the eccentricity line and the journal centerline, and profile height amplitude, ap.

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Fig. 2

Film thickness distributions due to the misaligned shaft with varying profile height amplitudes for β = 0.02 deg and ψ = 0 deg. The cross-sectional views at θ = θmin for each provides clearer local views of the film thicknesses at y/L = 1. (a) Cylindrical shaft that is unprofiled; Ap = 0, ∂h/∂y < 0 at (θ = θmin, y/L = 1). (b) Profile height less than the tangent profile height; Ap = 0.24, ∂h/∂y < 0 at (θ = θmin, y/L = 1). (c) Profile height equal to the tangent profile height; Ap = 1, ∂h/∂y = 0 at (θ = θmin, y/L = 1). (d) Profile height larger than the tangent profile height; Ap = 2.4, ∂h/∂y > 0 at (θ = θmin, y/L = 1).

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Fig. 3

Flowchart of simulation. There are two main nested loops: the Reynolds equation convergence loop and the load balance loop. The outer most loop is the time loop.

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Fig. 4

Model verification: (a) transient displacements match well with the results from Ausas et al. [37] and (b) loads when considering the roughness flow factors match well with the results from Jang et al. [38]

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Fig. 5

Impulse load is applied. Four loading cycles are shown, and the peak vertical load is 20.6 kN.

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Fig. 6

Behaviors of four designs viewed in the variations of the minimum film thickness and friction. For β = 0.02 deg and ψ = 0 deg: (a) profile height effect on minimum film thickness, showing that film thickness can be enhanced with profile design and (b) profile height effect on total friction, showing that the peak frictions drop significantly with profiled design. Ap = 1 yields the largest film thickness improvement and peak friction reduction.

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Fig. 7

Pressure distributions at Θ = 1298 deg. For β = 0.02 deg and ψ = 0 deg: (a) pressure contour for the unprofiled case (Ap = 0). Boxed area shows high pressure peak caused by misalignment. (b) Pressure contour for profiled case (Ap = 1). The pressure peak is significantly reduced. (c) Circumferential direction pressure distribution containing the maximum pressure. (d) Axial direction pressure distribution containing the maximum pressure. The profile design of Ap = 1 helps lower the pressure peak and redistribute the pressure closer to the center of the bearing so that lower pressure needs to be sustained by the film at the edge.

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Fig. 8

Influences of profile height amplitude on friction. For β = 0.02 deg and ψ = 0 deg: (a) Couette friction, (b) Poiseuille friction, and (c) asperity friction.

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Fig. 9

Parametric study plots for varying profile height amplitude. For β = 0.02 deg and ψ = 0 deg: (a) bearing performance metrics in terms of the minimum film thickness and (b) mean friction components.

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Fig. 10

Parametric study plots for varying misalignment angle. For ψ = 0 deg: (a) bearing performance metrics in terms of the minimum film and average and peak frictions and (b) mean friction components of the mean Couette, Poiseuille, and asperity frictions.

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Fig. 11

Film thicknesses of varying β and ψ values. The bolded line in each plot connects the lowest film thickness at each point across the axial width direction of the bearing. For ψ = 45 deg and β = 0.02 deg, film thicknesses are shown in (a) with Ap = 0 and (b) with optimal profile, Ap = 1. For ψ = 90 deg and β = 0.02 deg, film thicknesses are shown in (c) with Ap = 0 and (d) with optimal profile, Ap = 0.2. For ψ = 90 deg and β = 0.04 deg, film thicknesses are shown in (e) with Ap = 0 and (f) with optimal profile, Ap = 0.3.

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Fig. 12

Influence of RMS roughness on (a) bearing performance metrics and (b) mean friction components. For β = 0.02 deg and ψ = 0 deg.

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Fig. 13

Parametric study for the rotational speed. For β = 0.02 deg and ψ = 0 deg, bearing performance metrics in terms of minimum film thickness, mean friction, and peak friction.

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Fig. 14

Friction variations with shaft rotational speed. For β = 0.02 deg and ψ = 0 deg, the mean Couette, Poiseuille, and asperity frictions are plotted.

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Fig. 15

Wear load plots. For β = 0.02 deg and ψ = 0 deg. (a) Unprofiled case. The wear load peak is shown by the zoomed-in view. (b) Profiled bearing case (Ap = 1). Wear is expected at bearing end of the unprofiled journal case. No significant wear load is observed in the entire domain of the profiled shaft.

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Fig. 16

Transient misalignment parameters: (a) β variation from an initial value of β = 0.01 deg, peaked at β = 0.0275 deg and (b) ψ variation from an initial value of ψ = 0 deg, peaked at ψ = 180 deg

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Fig 17

Results for transient misalignment parameters. Minimum film thickness and total friction results against rotation angle for a profiled (Ap = 1) and unprofiled (Ap = 0) cases. (a) An approximately 200% increase in min(hmin) with the addition of the profile. (b) A 12% decrease in the peak friction and a 5% increase in the mean friction with the addition of the profile.

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Fig. 18

Computational stencil for discretization

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