Extension of the Reynolds equation by a non-linear wall slip regulation

When an electrical car accelerates, the motor generates most forces and large pressures act on the gears of the electrical drivetrain. Floor meets floor, metallic meets metallic. If there have been no lubricating movie to permit the gears to slip extra simply, they might not solely grow to be extraordinarily sizzling however would additionally put on out shortly. “With out a lubricating movie, many issues in our on a regular basis lives can be slower, squeakier, and jerkier,” explains Prof. Michael Moseler, Head of the Tribology Enterprise Unit on the Fraunhofer IWM.

“The electrical car will surely by no means obtain such a excessive vary,” provides Dr. Kerstin Falk, who heads the “Molecular Lubrication Design” staff. Collectively, they’re researching the conduct of lubricating movies in extremely pressured tribological contacts to be able to predict their suitability for low-friction operation.

Whether or not the fabric in query is metallic, plastic, or ceramic, superb lubrication can save over 20 % of power as machines run with much less resistance. That is additionally a promising subject of analysis by way of sustainability.

It’s, subsequently, no surprise that the accomplice firms of the MicroTribology Heart µTC, a collaboration between the Fraunhofer IWM and the Karlsruhe Institute of Know-how (KIT), are very eager about decreasing friction of their methods as a lot as potential.

“Many tribological methods at the moment are being designed at their load restrict, the place lubricating movie thicknesses within the nanometer vary and pressures within the gigapascal vary happen. Our companions are questioning learn how to calculate the friction in a part with such extremely loaded tribological contacts, as standard fluid dynamic calculation approaches fail underneath these excessive circumstances,” says Kerstin Falk, summarizing the issue.

Along with their simulation staff on the MicroTribology Centrum μTC, Falk and Moseler have discovered a solution to this query. They’ve printed their analysis in Science Advances.

Understanding and optimizing friction

How friction could be calculated and thus stored as little as potential is determined by the lubrication regime an organization goals for in its parts. Often, it desires to drive its tribosystems—the place a drive presses the first and counter our bodies collectively—underneath elastohydrodynamic circumstances.

A lubricating movie, the thickness of which is far better than the roughness of the 2 surfaces, is meant to scale back friction. On this case, the friction could be precisely predicted utilizing a continuum mechanics method. This entails fixing the so-called Reynolds equation for the lubricant, which Osborne Reynolds derived in 1886.

As well as, the warmth conduction equation for the general system and the linear elastic equations for each surfaces are calculated. The one materials information required are the moduli of elasticity and Poisson’s ratios of the friction companions, thermal conductivities and warmth capacities of all supplies concerned, in addition to correct constitutive legal guidelines—for the density of the fluid and for its dynamic viscosity for a parameter subject consisting of strain, temperature and native shear price within the fluid. That is cutting-edge.

Nevertheless, if the tribological system is operated in boundary lubrication, with a really skinny lubricant movie through which the asperity contacts, i.e., the roughness peaks, are solely separated by a number of atomic layers of the lubricant, solely a roughly estimated coefficient of friction is used within the calculations for the “dry” contact factors.

“That is very unsatisfactory as a result of calculations with guessed materials parameters are inaccurate, result in suboptimal designs, and in the end price firms some huge cash,” says Michael Moseler.

Kerstin Falk and Michael Moseler weren’t content material with this: Along with 4 accomplice firms of the MicroTribology Centrum µTC, they researched their very own mathematical regulation for the conduct of extraordinarily skinny lubricating movies in a three-year mission and developed the Reynolds equation additional, so to talk. “We wished to know how friction behaves in boundary lubrication,” explains Moseler.

The intention of the mission is to make clear under which lubricating movie thickness the continuum mechanics fails and the way the underlying equations could be prolonged so {that a} lubricating movie thinner than the floor roughness could be calculated.

For this function, the molecular dynamics of a hydrocarbon lubricant in an asperity contact geometry have been calculated, for instance, two diamond-like carbon (DLC) surfaces lubricated with a polyalphaolefin (PAO) base oil. The outcomes of the molecular dynamics simulation have been then in contrast with these of the Reynolds equation.

The resounding end result: For pressures between the friction companions under 0.4 gigapascals and lubrication hole heights better than 5 nanometers, the Reynolds description agrees effectively with the molecular dynamics reference calculations, supplied that an actual constitutive regulation for the viscosity of the lubricant is used.

In distinction to this, Kerstin Falk and Michael Moseler have been capable of present that underneath excessive boundary lubrication circumstances, particularly excessive pressures of approx. 1 gigapascal and small lubrication hole heights of approx. 1 nanometer, the sticking of the lubricant to the surfaces is lowered, and subsequently, the slip between a friction accomplice and the lubricant should be included within the calculation to appropriately predict the friction.

This requires a non-linear wall slip regulation. This relates the wall slip velocities (i.e., the distinction in velocity between a friction accomplice and the adjoining lubricant) to the native shear stresses within the lubricating movie.

Breakthrough in tribology: Making boundary friction predictable

With these analysis outcomes, the researchers at the moment are presenting an revolutionary methodology for predicting friction underneath boundary lubrication circumstances. An extra piece of knowledge required for this non-empirical predictive continuum modeling of extremely loaded tribological contacts is the atomic construction of the rubbing surfaces. That is decided utilizing in-depth experimental analyses and is a prerequisite for the wall slip regulation.

The brand new findings of the Fraunhofer IWM at the moment are being utilized in follow-up initiatives to foretell friction coefficients and friction conduct in particular functions—for instance, in gears and bearings—in addition to to help the analysis companions in build up simulation experience.

They’ll then perform take a look at bench and part simulations, cut back uncertainties within the design of tribological methods, and extra exactly decide design parameters. That is a vital step in the direction of knowledge-based lubricant, floor, and part design and will show to be extraordinarily fascinating for lubricant producers and coaters in addition to bearing and equipment producers.