Study on Changes in the Rheologic Properties of EHL Film Using Fluorescence Measurements

Abstract

This article describes a fundamental study using the fluorescence measurement method to understand the rheologic properties (such as viscosity and solidification) of elasto-hydrodynamic lubrication (EHL) film. The measurement principle is based upon the excimer emission of a pyrene fluorescence agent, which depends on the viscosity. To investigate the relationship between the excimer emission and viscosity, the measurements were taken under low temperature, with the results showing that the excimer emission decreased with decreasing temperature because of increasing of viscosity. No remarkable peak was observed below the temperature at which the state changed from liquid into a viscoelastic or elastic–plastic solid. The fluorescence was clearly observed in EHL film, and its spectrum revealed that the intensity of excimer emission decreases along the flow direction, with a contact area having the same behavior as that of the elastic–plastic solid at 243 K. These results suggest that the viscosity increased at the inlet of contact because of increasing hydrodynamic pressure under the wedge action and that the state in the contact region changes to solid because of high contact pressure. This study also proposes that this measurement method can be used to understand the viscosity change and solidification in the lubrication film.

Appendix

In this study, a one-dimensional Ertel-Grubin calculation is used as a simple simulation model. The calculation model is shown in Fig. 13. The calculated part is the region from the start of the lubricated zone x₁ to the inlet position of the contact x₂. A value of 5 mm is assumed for x₁ based on the location of the outlet meniscus.

Fig. 13

Model for the calculation of pressure distribution at the inlet of the contact

In Ertel-Grubin’s equation [47], a one-dimensional modified Reynolds equation is described by following Eq. (5), which uses a reduced pressure, p₀, defined in Eq. (6). In Eq. (5), h _m is an integration constant.

$$\frac{{{\text{d}}p_{0} }}{{{\text{d}}x}} = 12\eta_{0} U\frac{{h - h_{m} }}{{h^{3} }}$$

(5)

where

$$p_{0} = \frac{1 - \exp ( - \alpha p)}{\alpha }$$

(6)

where α and U are the pressure-viscosity coefficient and rolling speed, respectively.

The film shape, h(x), is assumed to be described by Eq. (7) [47].

$$h(x) = h_{0} + \frac{{a^{2} }}{{\pi R_{\text{B}} }}\left( { - \left( {2 - \frac{{x^{2} }}{{a^{2} }}} \right)\cos^{ - 1} \frac{a}{x} + \left( {\frac{{x^{2} }}{{a^{2} }} - 1} \right)^{0.5} } \right)$$

(7)

where R_B is the equivalent radius of the ball and a is the radius of Hertzian contact under the test condition. The value measured using optical interferometry was used as h₀.

The reduced pressure p₀ distribution can be obtained by integrating Eq.(5), in which the boundary conditions p₀ at x₁ and x₂ are assumed to be zero and 1/α, respectively.

$$p_{0} = 12\eta U\left( {\int_{{ - x_{1} }}^{{ - x_{2} }} {\frac{1}{{h^{2} }}{\text{d}}x - h_{m} \int_{{ - x_{1} }}^{{ - x_{2} }} {\frac{1}{{h^{3} }}{\text{d}}x} } } \right)$$

(8)

where

$$h_{m} = \frac{{\int_{{ - x_{1} }}^{{ - x_{2} }} {\frac{1}{{h^{2} }}{\text{d}}x} - \frac{1}{{12\eta_{0} U\alpha }}}}{{\int_{{ - x_{1} }}^{{ - x_{2} }} {\frac{1}{{h^{3} }}{\text{d}}x} }}$$

(9)

The value of the viscosity (2.5 Pa s at 295 K [48]) and pressure-viscosity coefficient (54 GPa⁻¹ at 295.5 K [14]) are the same as those under experimental conditions.

Finally, the pressure p and viscosity ratio, η/η₀, are given by Eqs. (10) and (11).

$$p = \frac{1}{\alpha }\left\{ { - \ln \left( {1 - \alpha p_{0} } \right)} \right\}$$

(10)

$$\frac{\eta }{{\eta_{0} }} = \exp (\alpha p)$$

(11)