Mixed EHL Lubrication There are situations where both boundary lubrication and full film lubrication play an important role in the overall lubrication of the contacting bodies. The lubrication regime between boundary and elastohydrodynamic lubrication is termed as partial EHL or mixed EHL. Partial EHL deals with the simultaneously occurring solid to solid contact and elastohydrodynamic lubricated contact. It is generally believed that if the average film thickness is less than three times the composite surface roughness, the surface asperities will force direct solid to solid contact, resulting in mixed-EHL. A dimensionless film parameter is defined to distinguish the lubrication regimes possible for rough surfaces lubrication:

2,

2,

min

bqaq RRh

+= (17)

where hmin is the minimum lubricant film thickness, Rq,a and Rq,b are the root mean square surface finish of contacting bodies respectively. The lubrication regimes are characterized as:

5 100 - hydrodynamic lubrication3 10 - elastohydrodynamic lubrication

1 5 - partial or mixed lubrication1 - boundary lubrication

met in the past decade. To study such an EHL problem when surface features protrude through the lubricant film, a mixed contact model is needed. Jiang et al. (1999) presented a deterministic mixed contact models and investigated solid to solid contact of surface asperities or features as they moved through an EHL contact region. In their models, the solid contact pressure was calculated using inverse FFT method. More recently, Wang et al. (2004) used a macro-micro model to study mixed EHL, which superimposed off-line asperity contact pressure calculation on to the elastohydrodynamic pressure determination from the average flow model developed by Patir and Cheng (1978). Hu et al. (1999) developed a deterministic mixed EHL model. Figure 9 depicts the pressure and film thickness distribution for a mixed EHL contact. The pressure distribution along the center of contact in the rolling direction is also shown. The results show that the pressure undergoes large fluctuations where there is surface asperity contact. The orthogonal shear stress along the center line of contact in the rolling direction is also shown to demonstrate the effect of surface asperities on internal stresses. For lower average film thickness (ha/Rq 0.5GPa), the lubricant film propagates through the contact area with the mean surface velocity. It is consistent with the analysis of the Reynolds equation that for heavily loaded contacts, the high pressure causes the pressure terms in the Reynolds equation to vanish and it simply becomes:

0=

+

t

hx

hum

(18)

For most lubricants, the effect of compressibility is minimal and can be neglected. Thus the solution to the above equation is: h h(x-umt), which demonstrates that the film profile moves to the right with a velocity of um. The overall film thickness propagation for the start up process is shown in Figure 11 for the experimental results (Glovenea and Spikes, 2001), together with the

analytical and numerical results. Figure 12 depicts the film thickness and pressure distributions at the beginning, an intermediate, and the final instants during the start up process. The solid and lubricated contact regions can be clearly visualized during the EHL start up process. The start up time, defined as the time in which both the solid contact and the lubricated contact are simultaneously occurring, can simply be determined for a linear acceleration (constant acceleration rate) start up as: