Rough Surface Contact of Curved Conformal Surfaces: An Application to Rotor–Stator Rub

Rotating machines and associated triboelements are ubiquitous in industrial society, playing a central role in power generation, transportation, and manufacturing. Unfortunately, these systems are susceptible to undesirable contact (i.e., rub) between the rotor and stator, which is both costly and dangerous. These adverse effects can be alleviated by properly applying accurate real-time diagnostics. The first step toward accurate diagnostics is developing rotor–stator rub models which appropriately emulate reality. Previous rotor–stator rub models disavow the contact physics by reducing the problem to a single esoteric linear contact stiffness occurring only at the point of maximum rotor radial deflection. Further, the contact stiffness is typically chosen arbitrarily, and as such provides no additional insight into the contacting surfaces. Here, a novel rotor–stator rub model is developed by treating the strongly conformal curved surfaces according to their actual nature: a collection of stochastically distributed asperities. Such an approach is advantageous in that it relies on real surface measurements to quantify the contact force rather than a heuristic choice of linear contact stiffness. Specifically, the elastoplastic Jackson–Green (JG) rough surface contact model is used to obtain the quasistatic contact force versus rotor radial deflection; differences and similarities in contact force between the linear elastic contact model (LECM) and JG model are discussed. Furthermore, the linear elastic model's point contact assumption is assessed and found to be inaccurate for systems with small clearances. Finally, to aid in computational efficiency in future rotordynamic simulation, a simple exponential curve fit is proposed to approximate the JG force–displacement relationship.