Metal pitting by the numbers

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May Not Make Headlines, But Rolling Contact Fatigue Is A Major Issue For Devices And Machines With Gears, Bearings, And Other Parts Involved In Frequent MotionA Flint, Mich. college professor has developed a mathematical formula to help more accurately predict lubrication needs.

Dr. Ilya  Kudish, professor of Mathematics at Kettering University, cites rolling contact fatigue – more commonly called pitting – as a major issue for any engine or machine with gears, bearings, and other parts involved in frequent motion, and he is one of an elite group of 17 other international experts working to identify research models to solve the physical problems associated with rolling contact fatigue.

“I have made progress on the serious problem of lubrication,” said Kudish of his second book on the topic of elastohydrodynamic lubrication which is one of the major factors affecting contact fatigue, a 700-page volume titled “­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­Elastohydrodynamic Lubrication for Line and Point Contacts.  Asymptotic and Numerical Approaches,” due out in June of this year.  His first book, “Modeling and Analytical Methods in tribology,” was a 900-page tome co-written with Dr. Michael J. Covitch, a chemist for Lubrizol.

Tribology is the science and engineering of interacting surfaces in relative motion, including the study and application of the principles of friction, lubrication and wear. Contact fatigue, or pitting, is caused by material defects and repeated stresses occurring in material and exacerbates defects and cracks in metal.

“Lubrication problems in contact fatigue are so complex they can only be solved numerically,” Kudish said. “It is virtually impossible to find precise analytical solutions because one of the challenges is having to solve problems described by integro-differential equations.”

One common problem requiring lubrication solutions is found in truck and transport.

“Requirements are getting more stringent on such types of equipment as bearings, gears…” said Kudish. “They have to be able to carry heavier loads than ever before. I have made progress in reducing the two-dimensional (point), heavily-loaded lubrication problem to a one-dimensional (line), heavily-loaded lubrication problem.”

What this means is that researchers can now better understand what is happening in the lubricated context of contact fatigue.

Kudish said he used analytical methods first followed by numerical methods. The numerical methods for solving the isothermal elastohydrodynamic lubrication (EHL) problems for heavily-loaded contacts are generally unstable. It turns out, he said, by using the combined analytical and numerical approaches it is possible to come up with a simple formula creating a clear, physical sense of regularization which leads to stable solutions of isothermal heavily -loaded point and line EHL problems. This two-pronged approach has already enabled him to derive analytical formulas for lubrication film thickness which can be used by experimentalists in the field.

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