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Contact Fatigue by the Numbers: Kettering University Professor Develops Mathematical Key to Solve the Problem of Predicting Lubrication Conditions When Transferring High Power or Transporting Heavy Loads.


Kettering University Mathematics Professor Ilya Kudish has developed the mathematical key to unlock a problem faced daily by those engaged in transferring high power or transporting heavy loads – predicting lubrication conditions.

Lubrication solutions for transferring high power/transporting heavy loads are a major challenge for the global economy and commerce. “Requirements are getting more stringent on types of equipment such as bearings, gears, etc.,” said Kudish, a professor of Mathematics at Kettering University. “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 problems to the corresponding one-dimensional (line), heavily-loaded lubrication problems.” What this means is that researchers can now better understand what is going on in the lubricated contacts subjected to wear and contact fatigue, Kudish explained.

Contact fatigue is a major topic in the field of tribology, 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, exacerbates defects and cracks in metal. It is caused by inherent material defects and repeated stresses occurring in material.

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Wear and contact fatigue in machinery subjected to heavy loads has traditionally been difficult to predict. One of the elements necessary to better predict wear and contact fatigue is a good knowledge of the processes going on in lubricated contacts. Unfortunately, the numerical methods for solving the isothermal elastohydrodynamic lubrication (EHL) problems for heavily-loaded contacts in bearings and gears are generally unstable, Kudish continued.

Kudish has developed a combined analytical and numerical approach resulting in a clear, simple physical sense of regularization, which leads to stable solutions of isothermal heavily-loaded point and line EHL problems.

This dual approach has already enabled him to derive analytical formulas for lubrication film thickness. These can be used by experimentalists in the field for analyzing EHL contacts lubricated by fluid lubricants with different rheologies under isothermal and thermal conditions.

His dual approach to point and line EHL problems for heavily loaded contacts is reflected in his second book about the field of tribology, a 700-page volume titled “Elastohydrodynamic Lubrication for Line and Point Contacts. Asymptotic and Numerical Approaches,” due out in June of this year.

About Kettering University

Kettering University in Flint, Mich., is a nationally-ranked STEM (Science, Technology, Engineering and Mathematics) and Business university and a national leader in combining a rigorous academic environment with rich opportunities for experiential learning and cooperative education. Kettering focuses on the learning experience of the individual student. For more information, visit

Kettering University
Dawn Hibbard, 810-762-9865

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