# Professor Develops Mathematical Key to Predict Lubrication Conditions

Tags: bearing lubrication, gear lubrication

A Michigan professor has developed a mathematical key for predicting lubrication conditions, helping to solve a problem faced by those engaged in transferring high power or transporting heavy loads.

"Requirements are getting more stringent on types of equipment such as bearings, gears, etc.," said Ilya 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."

This new approach should enable researchers to better understand what is happening in the lubricated contacts subjected to wear and contact fatigue, Kudish explained.

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

Kudish's dual approach to point and line EHL problems for heavily loaded contacts is reflected in his new book titled "Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches," which is due out later this year.