Page 24 - Oil and Gas Simulations
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SHAPE CHANGING                                                                              	 For a lubricated line contact, such as the
                                                                                            sliding of a cylinder against a flat surface

LUBRICANTS                                                                                  under steady loading conditions, any
                                                                                            equations used need to take into account
                                                                                            numerous attributes. These include

                                                                                            lubricant oil film thickness at different

Until recently, Shell was using propriety programs to                                       positions in relation to the contact, the
                                                                                            corresponding pressure that determines
model friction in lubricants for the automotive industry.
                                                                                            lubricant density, lubricant dynamic

However, as the complexity of their simulations increase,                                   viscosity, the relative speed of moving
the engineering team at Shell has turned to multiphysics                                    surfaces, the reduced radius of curvature
                                                                                            for the contacting surfaces, the reduced

simulation to develop more in-depth analyses.                                               Young’s modulus of the surfaces, and the
                                                                                            load per unit length.

by JENNIFER HAND                                                                            	 “We end up with some rather complex
                                                                                            analytical expressions for the elastic

                                                                                            deformation of a medium due to an

Lubricants that can deliver better fuel        causing metal surfaces to deform             applied pressure at the surface,” describes
economy or improved energy efficiency          elastically. As a consequence of these two   Taylor. “It is also worth pointing out that
are in demand and the market is huge.          effects, the oil film thickness is greater   lubricant viscosity is a strongly varying
Independent consultants Kline & Company        than otherwise expected, which is exactly    function of pressure. The numerical
estimate that the global requirement for       why such high pressure contacts can be       solution of these equations is not
lubricants in 2010 was almost 38 million       successfully lubricated. The fact that high  straightforward since the character of the
tons, approximately 44 billion liters.         pressure promotes lubrication rather than    partial differential equation changes at
	 According to Dr. Robert Ian Taylor,          hinders it can seem a bit non-intuitive.     different points in the contact.”

Technology Manager at Shell Research in        The key is to account for these two effects  èINCORPORATING ANALYSIS
the UK, a reduction in lubricant viscosity     when predicting performance.”                TO BETTER UNDERSTAND
is regarded as one of the key approaches       	 This type of lubrication is known as       LUBRICATION PROBLEMS
to improving energy efficiency, and the        elastohydrodynamic lubrication and
choice of base oil is significant. “There      as Taylor notes, it is no easy matter to     Finite element analysis, using a
is a move towards synthetics, in which         measure lubricant rheology, or flow,         multiphysics solver, is an approach for
molecules are highly controlled, often by      under such pressures, especially as shear    taking into consideration all of the
the further processing of mineral-based        rates can also be as high as 108 s-1. “In    participating properties. “We wanted
oils. ‘Slippery’ chemical additives, called    elastohydrodynamically lubricated            to solve the Reynolds’ equation on the
friction modifiers, are also being used.”      contacts, we generally have much thinner     contact line or surface; find the pressure in
                                               films than one micron, so shear rates are    the lubricant; use that calculated pressure
èTHE BENEFITS OF                               correspondingly higher. Any mathematical     to analyze the elastic deformation in the
ELASTOHYDRODYNAMIC                             models we develop must be capable            underlying surface; then use the changed
LUBRICATION                                    of allowing for varying rheological          surface shape to recalculate the pressure
                                               descriptions of the lubricant.”              distribution (see Figure 1).”
In general, energy efficient lubricants

deliver lower friction because the oil film

thickness in the contact is reduced. Of

course, if oil film thickness is reduced too

much, there is the possibility of higher

wear. It is therefore particularly important

to be able to predict the effect of lubricant

properties on the thickness of the oil film

and the friction of a lubricated contact.

	 “For lubricated contacts, such as plain

journal bearings or piston rings, and at

pressures below 200 MPa, the Reynolds’

equation can easily be solved to predict

oil film thickness and friction,” comments

Taylor. “However, there are many

important lubricated contacts, such as

gear teeth or rolling element bearings,

where extremely high pressures of up

to 3 or 4 GPa can be generated in the          FIGURE 1. Schematic of multiphysics approach to solving lubrication problems. The

lubricant.                                     Reynolds’ equation is solved on the line, or surface. The calculated pressure distribution is

	 Under such pressures the viscosity           then used to calculate elastic deformations and this process is repeated until convergence

of the lubricant increases dramatically,       is obtained.

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