Application of fractional calculus to tribological analysis of magnetic fluid-Based parallel plate slider bearing

Fractional calculus has also developed itself as an effective mathematical representation of modeling complex dynamic systems with memory and hereditary behaviour with important advantages in tribological application where integer-order models do not exhibit micro- and nanoscale effects. Although there has been a lot of study on the ferrofluid lubrication and bearing systems, the integration of the fractional-order derivatives to explain the memory effects and non-local behavior in magnetic fluid-based lubrication has not been pursued especially in parallel plate slider bearings in micro/nanoscale. This paper shows an analytical research on pressure distribution and load carrying capacity in ferrofluid-lubricated parallel plate slider bearings based on the theory of fractional calculus through Riemann-Liouville approach. Fractional-order derivatives (order α ) are used to modify the classical Reynolds equation to capture the effects of the memory in the ferrofluid lubricant film, and enhance the representation of the fluid behavior in the micro and nanoscale environments. The Neuringer-Rosensweig ferrohydrodynamic theory gives the modified fractional Reynolds equation solved analytically based on the Riemann-Liouville framework of the fractional calculus. Findings show that the fractional-order parameter, which changes the percentage of pressure distribution and load-carrying capacity significantly, becomes minimal when the fractional-order parameter, defined as α , is reduced, and the changes are 10-15 percent lower than the changes in classical models ( α = 2.0). It is shown that the magnetization parameters and the dynamics of the fractional-order are closely coupled and allow regulating the performance of the bearings with the help of the external magnetic fields. The fractional-order modeling technique offers a good and more flexible alternative to designing and optimizing magnetic fluid-based bearing systems and has been directly applied to precision machinery, aerospace, and biomedical engineering systems where improved tribological behavior and controllability are of utmost importance.