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Research Papers: Mixed and Boundary Lubrication

# Theoretical Modeling for Microgrooved Journal Bearings Under Mixed Lubrication

[+] Author and Article Information
Katsuhiro Ashihara

Research Department, Taiho Kogyo Co., Ltd., 2-47 Hosoya-Cho, Toyota-City, Aichi Prefecture, 471-8502, Japanashihara@taihonet.co.jp

Hiromu Hashimoto

Tokai University, 259-1292, Japan

J. Tribol 132(4), 042101 (Oct 07, 2010) (16 pages) doi:10.1115/1.4002214 History: Received February 25, 2009; Revised July 16, 2010; Published October 07, 2010; Online October 07, 2010

## Abstract

In designing of engine bearings for automobiles, we need to establish a mixed lubrication model that considers the solid-to-solid contact between journal surfaces and bearing surfaces with microgroove. However, as far as we know, there is no literature treating such problems. This paper describes theoretical modeling for microgrooved bearings under the mixed lubrication conditions with experimental verifications and prediction of performance in the actual engine bearings. In this modeling, a sectional shape of the microgrooved bearing was approximated to be a circular sectional shape. Contact pressure between the journal surfaces and the bearing surfaces with microgroove was calculated using the Hertzian contact model and the effects of elastic deformation of bearing surface due to hydrodynamic and contact pressures were considered. A numerical calculation model was developed to predict bearing performance under the mixed lubrication condition in microgrooved journal bearings. Oil film thickness distributions, hydrodynamic and contact pressure distributions, and real contact area between the journal surfaces and the bearing surfaces with microgroove were obtained simultaneously by the theoretical model. Moreover, friction coefficients under mixed lubrication conditions were determined by the theoretical model and the calculated results were compared with experimental results using test rig. The calculated results successfully agreed with the experimental results and the applicability of the model was verified. Moreover, the model was applied to predict the performance of engine bearings. In the numerical results, real contact area occurred relative widely under low-speed conditions when engine was started but friction loss was not excessive because of low shearing velocity. On the other hand, under high-speed engine conditions, the friction loss was large in spite of narrow real contact area because of high shearing velocity. Under both low-speed and high-speed conditions, the real contacts will occur severely at the edge of the bearing in the axial direction and at the bearing angles from 50 deg to 110 deg in circumferential direction. In addition, an appropriate design of the microgrooved bearing was examined under mixed lubrication conditions. In the design of the microgrooves, a cooling effect and an enough amount of oil flow to the contact area are needed. As the results from parametric studies using present theoretical model, an influence of the depth of the microgroove was the largest on the cooling effect and the enough amount of oil flow. In the case of typical operation condition, it was found that $1.0 μm$ of the groove depth was the most appropriate.

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## Figures

Figure 2

Cross-sectional configuration of microgroove approximated to trapezoid for calculation

Figure 3

Contact analytical model of microgroove approximated to circular arc and variables concerning contact property

Figure 4

Contact analytical model and each variable for the comparison between trapezoid and circular arc

Figure 5

Comparison of contact load between trapezoid model and circular arc model (lc=1.0 mm)

Figure 6

Comparison of flow factors between trapezoid and circular arc: (a) 1/4 truncated model, (b) 1/2 truncated model, and (c) 3/4 truncated model

Figure 7

Figure 8

Free body diagram of force equilibrium between applied load W and load carrying capacity at fluid region Wf and real contact region Wc: (a) equilibrium between W and (Wc+Wf) in bearing and (b) contact force wc and fluid film force wf

Figure 9

Flowchart of calculation of mixed lubrication problem

Figure 11

Test apparatus for experimental verification in this research

Figure 12

Figure 15

Load diagram for connecting rod bearing (inline-four-stroke cycle, automotive diesel engine)

Figure 16

Relationship between crank angle and predicted values of bearing characteristics in several rotational speeds (a=2.0 μm, lT=0.17 mm, and l2=0.035 mm)

Figure 17

Bearing characteristics under mixed lubrication bearing (a=2.0 μm, lT=0.17 mm, and l2=0.035 mm)

Figure 18

Sensitivity of design factors (clearance c=18−38 μm, pitch lT=0.05−0.4 mm, and depth a=0.5−4.0 μm): (a) sensitivity of design factors to oil flow, (b) sensitivity of design factors to power of shear stress, and (c) sensitivity of design factors to power of shear stress

Figure 19

Relationship between depth of MGB and oil flow ratio and power of shear stress ratio (clearance c=28 μm, pitch lT=0.17 mm): (a) Rotational speed is 1000 rpm. Crank angle is 10 deg. Bearing angle is 95 deg. (b) Rotational speed is 4500 rpm. Crank angle is 270 deg. Bearing angle is 55 deg.

Figure 20

Geometrical cross section of microgroove

Figure 1

Schematic view of microgrooved bearing

Figure 10

Relationship between microgrooves geometry and discrete points on bearing surface in present analytical model

Figure 13

Sectional topography of bearing surface after tests (at 315 min)

Figure 14

Comparison of friction coefficient between experiment and calculation (N=1300 rpm, α=1.25 μm, and lT=0.17 mm)

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