No slipping and sliding

From busy restaurants to quiet home kitchens, all it takes are a few drops of cooking oil on a tile floor to create a dangerously slick surface. Indeed according the Bureau of Labor Statistics (BLS), in the workplace alone, slip and fall accidents are one of the most common causes of injuries.

For over 20 years, the University of Pittsburgh professor Kurt Beschorner has applied bioengineering methods to help prevent such injuries. He recently collaborated with his colleague Tevis Jacobs and four Pitt scholars to test and validate an important model that can predict shoe-floor friction. Their research, published in the American Society of Mechanical Engineers Journal of Tribology, is titled “Validation of a Multiscale Hysteresis Mechanics Model in Predicting Oily Shoe-Floor Friction Across Surfaces with Varying Finishes” (DOI: 10.1115/1.4068109).

Their study presents valuable insight into shoe-floor-friction modeling that manufacturers can use to help improve workplace safety.

“To better predict shoe-floor friction, our team developed a model for simulating microscopic scale interactions between the floor and the shoe sole,” said Beschorner, who is associate professor and graduate program director of bioengineering at Pitt’s Swanson School of Engineering. “We had previously developed two scales, one for micrometer interaction and the other for the tread interaction with the ground. We first tried to expand this model to other scales that were relevant, but we had challenges that prevented the model from providing meaningful predictions.”

The team turned to a longstanding model of friction that was developed by Swedish tribologist Bo Persson. “It’s widely used by mechanical theorists but less so by experimental scientists,” said Beschorner. “It’s complex, and there hasn’t been much work to validate the model in the shoe-floor-friction community.”

Collaborating to determine the right scales

Essential to validating Persson’s model was the ability to characterize floor surfaces across many scales including the microscopic and nanometer scale. Beschorner and his two students Henry Ing and Anna Randolph turned to Jacobs, the William Kepler Whiteford Professor of mechanical engineering and materials science, and his students Vimanyu Chadha and Ky Reifler.

“To more accurately measure surfaces, it’s essential to use multiple methods and scales,” said Jacobs. “We used a stylus profilometer and scanning electron microscopy, or SEM. The former acts like a record player needle moving across the surface, recording changes in the topography. The latter involved us cutting floor surfaces, turning them on their side, polishing them, and scanning them with a beam of electrons.”

Asperities, or the rougher edges on surfaces, produce different frequencies, and shoe soles have materials with properties that are frequency dependent. To better understand the frequencies generated by the floor and a shoe sole’s ability to absorb them, which helps determine shoe-floor friction, they needed multiple scales of floor topography, which Jacobs and his students provided.

The team also needed to better characterize shoe materials, so they cut samples of rubber soles and sent them to C-Therm, a company that tests the thermal conductivity of materials such as polymers and composites. C-Therm performed dynamic mechanical analysis to help determine a shoe’s ability to absorb the energy produced by the asperity.

“Shoe frequency responds up to 150 kilohertz (150,000 cycles per second); unfortunately, there aren’t devices that can do it,” said Beschorner. “We tested up to 200 hertz (or 200 times per second). To reach the higher rate, you can use time-temperature superposition. By lowering the temperature of rubber, it responds as if the frequency has been increased, which allowed us to capture the frequency response across many scales.”

Modeling real-world scenarios

Central to this research was modeling friction in oily conditions on many surfaces. In the Human Movement and Balance Laboratory, which Beschorner directs, they tested three shoes and ten porcelain tiles, with each surface covered in canola oil.

In addition to providing a real-world scenario, the canola oil had a second, equally important rationale: “If you can design shoes and flooring to be safe on canola oil, they’re safe in a lot of other scenarios,” said Beschorner.

While he plans future research on other wet and oily surfaces, the study already has advanced shoe-floor-friction modeling. Through the many length-scales in the topography and the frequency scales measured in the shoe soles, the research has increased the predictive abilities of the model.

“We found the appropriate scales to implement Persson’s model—and it worked quite well,” Beschorner said. “We validated a complex theory and made it more applicable for manufacturers.”

Henry Ing, lead author and Beschorner’s master’s student at the time of the research, said, “We learned that to decrease slips and falls, manufacturers can modify how they characterize shoe materials. When characterizing outsoles, they need to do so for the range of frequencies corresponding to the proper surface asperity size scales. The ability to predict the impact of surface roughness and or shoe materials on friction can improve safety as well as aid in footwear development and floor manufacturing.”

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Honoring a mentor in tribology

The team’s research is published in a special issue dedicated to Dr. Michael Lovell, who passed away in June 2024. Lovell earned his PhD at Pitt, where he later served as the Associate Dean for Research. Beschorner met him as a PhD student at Pitt, and Lovell took the graduate student under his wing. Though Lovell wasn’t teaching a course in tribology at that point, he gave Beschorner weekly lessons and provided him with course materials.

Lovell left Pitt to serve as the dean of the engineering program at the University of Wisconsin-Milwaukee, and he recruited Beschorner to teach there. Before Lovell moved on to Marquette University, where he would become the school’s president, Beschorner had the opportunity to collaborate with his mentor.  

Today, Beschorner works with students like the four whose contributions were, as he said, “essential to the success of this project—from methodically breaking down complex models to testing the coefficient of friction to measuring the surfaces.” The opportunity to see his own students now advance the field of tribology only fuels the passion for the subject that Lovell helped ignite.