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RESEARCH PAPERS

# Thermal and Non-Newtonian Numerical Analyses for Starved EHL Line Contacts

[+] Author and Article Information
P. Yang

School of Mechanical Engineering, Qingdao Technological University, Qingdao 266033, China

J. Wang

Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan

M. Kaneta

Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japankaneta@mech.kyutech.ac.jp

J. Tribol 128(2), 282-290 (Jul 27, 2005) (9 pages) doi:10.1115/1.2164465 History: Received January 17, 2005; Revised July 27, 2005

## Abstract

This paper focuses on the mechanism of starvation and the thermal and non-Newtonian behavior of starved elastohydrodynamic lubrication (EHL) in line contacts. It has been found that for a starved EHL line contact if the position of the oil-air meniscus is given as input parameter, the effective thickness of the available lubricant layers on the solid surfaces can be solved easily from the mass continuity condition, alternatively, if the later is given as input parameter, the former can also be determined easily. Numerical procedures were developed for both situations, and essentially the same solution can be obtained for the same parameters. In order to highlight the importance of the available oil layers, isothermal and Newtonian solutions were obtained first with multi-level techniques. The results show that as the inlet meniscus of the film moves far away from the contact the effective thickness of the oil layers upstream the meniscus gently reaches a certain value. This means very thin layers (around $1μm$ in thickness) of available lubricant films on the solid surfaces, provided the effective thickness is equal to or larger than this limitation, are enough to fill the gap downstream the meniscus and makes the contact work under a fully flooded condition. The relation between the inlet meniscus and the effective thickness of the available lubricant layers was further investigated by thermal and non-Newtonian solutions. For these solutions the lubricant was assumed to be a Ree-Eyring fluid. The pressures, film profiles and temperatures under fully flooded and starved conditions were obtained with the numerical technique developed previously. The traction coefficient of the starved contact is found to be larger than that of the fully flooded contact, the temperature in the starved EHL film, however, is found to be lower than the fully flooded contact. Some non-Newtonian results were compared with the corresponding Newtonian results.

###### FIGURES IN THIS ARTICLE
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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic diagram of a staved EHL line contact

Figure 2

The relations of the effective thickness of the available oil layers and the central film thickness with the position of the air-oil meniscus of the isothermal and Newtonian solutions for U=1×10−11, G=4949, and W=4×10−5

Figure 3

Pressure distributions with various positions of the air-oil meniscus. From the highest spike to the lowest spike, the value of xin∕b is −3.6, −1.5, −1.25, −1.1, and −1.02, respectively. Isothermal and Newtonian solutions for U=1×10−11, G=4949, and W=4×10−5.

Figure 4

Film thickness profiles corresponding to the pressures given in Fig. 3. From top to bottom the value of xin∕b is −3.6, −1.5, −1.25, −1.1, and −1.02, respectively.

Figure 5

The relations of the effective thickness of the available oil layers and the central film thickness with the position of the air-oil meniscus of the thermal and non-Newtonian solutions for Σ=1.2, U=2×10−11, G=4949, and W=1.5×10−4

Figure 6

Pressure distributions with various positions of the air-oil meniscus. From the highest spike to the lowest spike, the value of xin∕b is −3.6, −1.25, −1.1, −1.04, and −1.01, respectively. Thermal and non-Newtonian solutions for Σ=1.2, U=2×10−11, G=4949, and W=1.5×10−4.

Figure 7

Film thickness profiles corresponding to the pressures given in Fig. 6. From top to bottom the value of xin∕b is −3.6, −1.25, −1.1, −1.04, and −1.01, respectively.

Figure 8

Temperature distributions in the middle layer of the film (solid line), and on surface a (dashed line) and b (dotted line) of the fully flooded (xin∕b=−3.6) contact. Thermal and non-Newtonian solutions for Σ=1.2, U=2×10−11, G=4949, and W=1.5×10−4.

Figure 9

The flow velocity distributions across the film at x=0 for xin∕b=−3.6 (solid line) and −1.01 (dashed line), respectively. Thermal and non-Newtonian solutions for Σ=1.2, U=2×10−11, G=4949, and W=1.5×10−4.

Figure 10

Temperature distributions in the middle layer of the film (solid line), and on surface a (dashed line) and b (dotted line) of the most severely starved (xin∕b=−1.01) contact. Thermal and non-Newtonian solutions for Σ=1.2, U=2×10−11, G=4949, and W=1.5×10−4.

Figure 11

Temperature contour map for the case of xin∕b=−1.1, numbers indicate the temperature in °C. Thermal and non-Newtonian solutions for Σ=1.2, U=2×10−11, G=4949, and W=1.5×10−4.

Figure 12

The variation in the traction coefficient versus the position of the air-oil meniscus for the same cases as in Fig. 5

Figure 13

Variations in the traction coefficients and the middle point temperatures versus the slide-roll ratios for the fully flooded and severely starved contacts. U=2×10−11, G=4949, and W=1.5×10−4, (a) traction coefficients, and (b) middle point temperatures.

Figure 14

Variations in the traction coefficients and the middle point temperatures versus the slide-roll ratios predicted by the Newtonian and Ree–Eyring solutions, respectively, for the starved contacts of xin∕b=−1.1, U=2×10−11, G=4949, and W=1.5×10−4, (a) traction coefficients, and (b) middle point temperatures

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