Stribeck curve

Stribeck curve
Name	Stribeck curve
Caption	A typical Stribeck curve showing the coefficient of friction as a function of the Hersey number.
Fields	Tribology, Mechanical engineering, Lubrication
Related	Richard Stribeck, Heinrich Hertz, Osborne Reynolds, Boundary lubrication, Hydrodynamic lubrication

Stribeck curve. The Stribeck curve is a fundamental concept in tribology that graphically represents the relationship between friction and lubrication regimes in sliding contacts. It plots the coefficient of friction against a dimensionless parameter, typically the Hersey number, which incorporates speed, viscosity, and load. This curve is essential for understanding the transition between boundary lubrication, mixed lubrication, and hydrodynamic lubrication, providing critical insights for designing efficient mechanical systems from internal combustion engines to artificial joints.

Definition and overview

The Stribeck curve characterizes how the friction coefficient in a lubricated contact varies with operating conditions, effectively mapping the lubrication regime. Its foundational parameter, the Hersey number, is derived from the work of Arnold Sommerfeld and later refined by M. D. Hersey. This curve is pivotal for engineers and researchers at institutions like the Massachusetts Institute of Technology and the University of Cambridge who study machine element performance. The curve's shape reveals the complex interplay between surface roughness, lubricant film thickness, and asperity contact, which dictates the energy efficiency and wear of components in systems ranging from gearboxes in Formula One cars to hard disk drive bearings.

Historical background

The curve is named after Richard Stribeck, a German engineer whose systematic experiments at the Royal Prussian Railway in the early 20th century quantified friction in railway journal bearings. His work built upon the foundational theories of Osborne Reynolds, who formulated the Reynolds equation for fluid film lubrication, and Heinrich Hertz, whose Hertzian contact theory described stress in non-conforming surfaces. Stribeck's findings were contemporaneous with the research of Beauchamp Tower and Nikolay Pavlovich Petrov, pioneers in tribology. The formalization of the curve was advanced later by G. Vogelpohl and became a cornerstone for organizations like the American Society of Mechanical Engineers and the Society of Tribologists and Lubrication Engineers.

Phases of the Stribeck curve

The curve is distinctly divided into three primary regimes dictated by the lambda ratio. In the **boundary lubrication** regime, prevalent at low Sommerfeld number values, the lubricant film is exceedingly thin, leading to direct asperity contact and high friction governed by surface chemistry and additive films. The **mixed lubrication** regime sees a decreasing friction coefficient as the fluid film begins to partially support the load, a transition critical in the startup of turbochargers and camshaft systems. Finally, the **hydrodynamic lubrication** or **elastohydrodynamic lubrication** regime is characterized by a thick lubricant film and friction dominated by fluid shear, essential for the operation of rolling-element bearings in wind turbines and gas turbine engines.

Factors influencing the curve

The precise shape and position of the Stribeck curve are influenced by numerous material and operational variables. Lubricant viscosity, affected by base oil composition and temperature, is a primary factor, as studied by Petro-Canada and ExxonMobil. Surface topography, including roughness average and texture directionality, plays a crucial role, with research conducted at the National Institute of Standards and Technology and the Fraunhofer Society. The applied load and the contact pressure, analyzed using Hertzian contact theory, significantly alter the transition points. Furthermore, the presence of extreme pressure additives, viscosity index improvers, and the elastic modulus of the contacting bodies, such as in polyethylene hip replacements, can dramatically modify the frictional response.

Applications and significance

The Stribeck curve is indispensable across a vast array of industrial and biomedical engineering applications. In the automotive industry, it guides the design of piston ring assemblies, valvetrain systems, and automatic transmission fluids to minimize fuel consumption. Within aerospace, it informs the lubrication of helicopter rotor bearings and aircraft engine components to ensure reliability. The curve is also critical in biomechanics for developing low-wear prosthetic materials used in the Mayo Clinic and Smith & Nephew implants. Its principles underpin standards set by the International Organization for Standardization and are taught globally in engineering curricula, from Stanford University to the Indian Institutes of Technology.

Measurement and characterization

Experimental determination of the Stribeck curve is performed using specialized tribometers, such as pin-on-disk testers and mini-traction machines, often within controlled environments at facilities like the Southwest Research Institute. Key measured parameters include the friction force, normal force, and sliding speed, which are used to calculate the Stribeck number. Advanced characterization employs optical interferometry techniques, pioneered at Imperial College London, to visualize film thickness. Computational fluid dynamics simulations, utilizing software from ANSYS and COMSOL, model the Navier-Stokes equations to predict curve behavior for novel materials like diamond-like carbon coatings tested by the NASA Glenn Research Center.

Category:Tribology Category:Mechanical engineering Category:Lubrication