On the Nonlinear Tribological Jerk Dynamics at Sliding Interfaces - (:unkn) unknown (My University, 2014)
As the world desires the next industrial revolution, the potential threats that will undermine energy efficient innovations include detrimental frictional effects that exacerbate wear, hasten equipment breakdowns, and worsen heat dissipation. Capturing the inherently nonlinear manifestations of friction fundamentally has been difficult. A fundamental modeling scheme elucidating friction will bolster novel technologies synthesizing wear resistant materials and lubricants needed for sustainable energy efficiency. Frictional dissipation at dynamical sliding interfaces has been studied for generations. Interfacial sliding frictional effects are prevalent in natural and artificial phenomena such as earthquake, hip and knee joints, and the moving parts of energy-producing and energy-consuming equipment. Hitherto, despite significant research efforts, no consensus fundamental modeling technique exists that deterministically ties friction with system degradation. Yet, elucidating the basic physics of nonlinear friction-resisted motion will clarify how heat generation, efficiency, lubrication, wear, and material lifetime evolve in sliding contacts. In this study, we unify Newtonian mechanics with classical thermodynamics to elicit nonlinear tribological jerk dynamics at a sliding interface. Jerk, the rate of change of acceleration has been elusive in classical mechanics. By showing jerk originating in a friction-resisted motion a new fundamental scientific modeling tool emerges. For example, although Coulomb's law of friction precludes significant friction-velocity coupling our reassessment using jerk dynamics results shows otherwise. We find Coulomb's law may seemingly be an oversimplification by reproducing the Stribeck effect known to capture friction-velocity coupling. Furthermore, negative frictional jerk opposes relative motion while positive lubricating jerk supports relative motion. A frictionless unconstrained motion recaptures constant acceleration Newtonian-Galilean mechanics. Using the kinematic and dynamic results as inputs, we quantified wear and wear rates, subsurface temperature and mechanical sliding efficiency. Our modeling results quantitatively match experimental results from tribometer and thermal compliance tests very well. We constructed an analytical algebraic partitioning technique to solve the jerk balance equations which are third order and nonlinear ordinary differential equations. The algebraic technique works well and may facilitate engineering and scientific modeling efforts. By placing jerk in basic physics context, we proffer a fundamental tool that likely will transform how relative motions in artificial and natural phenomena are modeled.
Keywords: Friction; Heat Generation; Jerk Dynamics; Lubrication; Mechanical Efficiency; Wear