Students in the Department of Mathematical Sciences partnered with Cummins Inc. to improve engine performance. Their challenge was to build a mathematical model to identify a narrow window when knock occurs in a four-stroke spark ignited engine. Knock is when a pocket of air and fuel mixes and combusts inside the cylinder at the wrong time, causing vibration and engine inefficiency.

Headquartered in Columbus, Indiana, Cummins, Inc. manufactures diesel and natural gas engines. Dr. Roza Aceska, Assistant Professor of Mathematical Sciences, cultivated this collaboration after spending time in Cummins, Inc. as a part of the Cardinal Connect Faculty Externship program. Pairing Ball State faculty with industry partners, the Cardinal Connect program allows faculty to examine work place practices and adjust curriculum, keeping it relevant and up to date.

Understanding the Problem

Undergraduate math students Cora Burkhardt, Malcom Harris, Kerry Hawken, Anna Hawkins and Brian Pierson made up the Optimization Team. Using data from Cummins, they developed formulas and a system to narrow down the precise moment when knock was occurring. Cummins can then use that information to make calculated improvements to their engine, reducing knock, and improving engine efficiency.

To begin working on the problem, the students first had to develop an understanding of how an engine works. After the team researched engine parts and became familiar with the problem, they created and tested models using the vibration data given to them by Cummins. Comparing their model formulas to a correlation set of data, the students were able to develop a formula that could closely pinpoint when knock would occur.

Team Work

Working with an industry partner on such a specific problem is beneficial for both the students and the company. Students are able to apply and develop their skills, such as critical thinking, analyzing data, and working in a team to solve a problem. Team member Anna Hawkins says, “My favorite thing about the course is team diversity. Our team consists of majors in pure math, applied math, and computer science. We have diverse interest even within those fields, along with other minors, and interests and external experiences. Each of us carries the team in a different way through our different roles, tasks, and commitments.”

The Optimization Team and Engineer, Jingxuan Liu, from the Cummins Technical Center are excited to continue the project through the summer. The students have an invitation to present their research and findings at the Math Fest in Cincinnati in August and plan to produce a journal article for publication. The students have already presented at the Ball State Student Research Symposium.

This project is supported by the Mathematical Association of America (MAA) via the MAA Pic Math program, which is funded by the National Science Foundation (NSF grant DMS-1722275) and the National Security Agency (NSA). PIC Math prepares mathematical sciences students for industrial careers by engaging them in research problems that come directly from industry.