Tribology in Industry a Historical Review of Gas Lubrication
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Vol. 40, No. 2 (2018), 165-182, DOI: 10.24874/ti.2018.40.02.01 Tribology in Industry www.tribology.rs VIEW RE A Historical Review of Gas Lubrication: From Reynolds to Active Compensations L. Lentini a, M. Moradi a, F. Colombo a a Department of Mechanical and Aerospace Engineering, Politecnico di Torino Corso Duca Degli Abruzzi 24, 10129, Turin, Italy. Keywords: A B S T R A C T Historical review Friction and wear are tribological phenomena that have produced Gas lubrication significant economic damage and environmental issues throughout our Aerostatic bearing history. Different kinds of lubricants and coatings have been employed in Active compensation the attempt of reducing friction losses. Because of their remarkable Passive compensation performance, gas lubricated systems are characterized by almost zero friction and wear. For this reason, they can be utilized in applications Corresponding author: where rolling and fluid bearings cannot, e.g., metrology, medical Luigi Lentini equipment and tool machine. This paper reviews the evolution of gas Department of Mechanical and lubrication through history. The topography of the subject is described Aerospace Engineering, Politecnico from its origins to how it was shaped over the centuries, trying to preserve di Torino, Corso Duca Degli Abruzzi the logical cause and effect relationship of the events. For the sake of 24, 10129, Turin, Italy. consistency, the review considers only the key past contributions which are E-mail: [email protected] strictly related to gas lubrication. © 2018 Published by Faculty of Engineering 1. INTRODUCTION performance, gas lubricants make it possible to significantly reduce friction and wear, thus Friction and wear are tribological phenomena providing systems with high positional that have produced significant economic accuracy and low environmental impact. For damage and environmental issues throughout this reason, gas lubricated systems are our history. The mechanical and thermal employed for high-precision applications, such severities caused by friction along with the as medical equipment and measuring and tool consequent wear are some of the most relevant machines [1,2]. problems faced by engineers in machine design. It is suffice to say that one-third of the fuel This paper reviews the history of gas consumption of passenger cars is used to lubrication. The topography of the subject is compensate frictional losses. Different kinds of described from its origins to how it was shaped lubricants and coatings are a solution currently over the centuries, trying to preserve the adopted to reduce friction and avoid the logical cause and effect relationship of the presence of wear. Because of their remarkable events. For the sake of consistency, the review 165 L. Lentini et al., Tribology in Industry Vol. 40, No. 2 (2018) 165-182 considers only the key past contributions which 1884) during his studying on the fluid flow are strictly related to gas lubrication. within brass tubes. The first part of the paper deals with the most In the same period, Claude Louis Navier (1785- important studies in fluid mechanics, i.e., the 1836) along with Sir George Gabriel Stokes took equation of motion and the equation of advantage of Euler and Poiseuille’s contributions continuity, which made it possible to lay the to provide one of the milestones of fluid foundations of lubrication theory. Secondly, the mechanics: Navier-Stokes Equations. paper describes the first experiments and 퐷푢 휕푃 휕2푢 휕2푢 휕2푢 theories on hydrodynamic lubrication and 휌 = 휌푋 − + 휇 ( 2 + 2 + 2 ) lubricant properties. The review continues by 퐷푡 휕푥 휕푥 휕푦 휕푧 focusing on the historical evolution of gas 2 2 2 퐷푣 휕푃 휕 푣 휕 푣 휕 푣 (2) lubrication up to today. 휌 = 휌푌 − + 휇 ( + + ) 퐷푡 휕푦 휕푥2 휕푦2 휕푧2 퐷푤 휕푃 휕2푤 휕2푤 휕2푤 휌 = 휌푍 − + 휇 ( + + ) 2. THE BEGINNING: THE BIRTH OF FLUID { 퐷푡 휕푧 휕푥2 휕푦2 휕푧2 MECHANICS This set of equations made it possible to model Although Daniel Bernoulli (1700-1782) was the the motion of viscous fluids by considering the first to publish a book in the field of fluid equilibrium between volume (inertial, mechanics: Hydrodynamica, sive De viribus et gravitational), pressure and viscous forces. motibus fluidorum commentarii, it is commonly recognised that the Swiss engineer Leonhard Euler (1707-1783) was the founder of the 3. FOUNDATION OF THE LUBRICATION subject. Driven by his passion for mathematics, THEORY: FROM EXPERIMENTS TO Euler was one of the most eminent scientists in REYNOLDS’ EQUATION history who provided the Equation of continuity and the Equations of motion for non-viscous Performing experimental studies on lubricant flows. This mathematical framework was the properties was the consequential and natural first step in laying the foundations of fluid film step of the development of the theoretical lubrication theory. The next step towards the framework by Navier and Stokes. Gustave formulation of the lubrication theory was Adolphe Hirn (1815-1890) was the first who provided by the French physician Jean Léonard investigated the frictional properties of different Marie Poiseuille (1799-1869), who analysed the kinds of fluids. He pioneered experimental properties of viscous fluids. He spent most of his works on fluid bearings by testing twelve life performing experimental investigations on natural oils (both mineral and fatty oils), air and blood flow in human capillaries. The result of water as lubricants. To perform these these arduous experiments was a formula to experiments, he developed a fine friction study viscous fluid flowing under laminar balance (Fig.1). regimes (Equation 1). According to Fig. 1, this friction balance consists 128 휇퐿푄 (1) of a half bronze bearing loaded against a Δ푃 = 4 휋푑 polished cylindrical cast iron drum. The bearing This equation made it possible to assess the supports a shaft that can rotate at different pressure drop within laminar flow through thin speeds and which is loaded with two dead pipes. He found that the pressure drop Δ푃 along weights applied at the extremities of two a straight capillary increases proportionally to horizontal lever arm of the same length. Given a the tube length 퐿, the fluid mass flow rate 푄 and constant rotational speed, frictional forces were viscosity 휇, and it decreases with the fourth measured by adding weights to balance the power of the conduit diameter 푑. Today, this misalignments between the two lever arms formula is known as Hagen-Poiseuille’s law since induced by friction. Performing these the same results were independently and experiments allowed Hirn to discover the contemporarily achieved by the German existence of the “frottement médiat” and the engineer Gotthilf Heinrich Ludwig Hagen (1797- “frottement immediate” regimes. 166 L. Lentini et al., Tribology in Industry Vol. 40, No. 2 (2018) 165-182 proportional to the speed, whereas, in the presence of high loads it varies approximately according to the square root of the speed. In addition, Hirn argued that also the temperature of the lubricant may have an important role. He noted that when the system worked for a long time, friction increased the lubricant temperature and consequently induced unbalances between the torque arms. According to this, he installed a water-cooled system CC’ (Fig. 1) that made it possible to keep the bearing temperature constant within plus or minus 0.1 °C, and unaware of Joule’s experiments, he also provided necessary measurements to change the water temperature by 1°C (3630 J with respect to the correct value measured by Joule 4090 J [4]). In 1879, Hirn’s studies were refined by Robert Henry Thurston (1839-1903). Thurston showed that, giving an increasing speed, the friction coefficient within a fluid bearing initially decreases below its static value, and reaches its minimum and then increases to a constant value. He also noted that the value of the minimum friction coefficient varied together with the applied load. Hirn and Thurston’s research was efficiently exploited by the Russian engineer Nikolay Pavlovitch Petroff (1836-1920). Petroff laid the Fig. 1. Hirn’s experimental apparatus for frictional foundation of the hydrodynamic theory of measurements. friction and carried out further viscosity measurements with the aid of an experimental He observed that the “frottement médiat” occurs apparatus similar to the one employed by when a full fluid film separates the surfaces in Poiseuille. His most important contribution was the presence of relative motions, i.e., providing the first analytical formulation to hydrodynamic regimes, whereas the “frottement evaluate friction coefficients in the presence of immediate” takes place in dry interactions or hydrodynamic lubrication. Petroff’s formula when the fluid film lubricant is broken. correlates the friction force and bearing parameters: “For water and air to act as lubricant it is 휇푈퐴 necessary for the drum to turn sufficiently rapidly 퐹푣 = 휇 휇 (3) to drag them into the bearing. When the speed 휀 + + 휆1 휆2 reduces to a certain value, the two non-viscous fluids are expelled by the pressure and the where, 휀 and 휇 are the film thickness and surfaces come into direct contact, and friction at viscosity of the lubricant, 푈 is the tangential once becomes enormous [3]” relative velocity between the interacting surfaces and 퐴 is the contact area. The By experimenting with different operating coefficients 휆1 and 휆2 consider slip phenomena conditions and lubricants, Hirn discovered that at walls of the interacting surfaces. Despite much under the hydrodynamic regime, friction effort devoted to performing studies on coefficients depend on the rotational speed, load hydrodynamic lubrication, Petroff was not able and lubricant properties. In the presence of full to find the relation that exists between friction film lubrication and light loads, friction is and the load carrying capacity of a fluid bearing. 167 L. Lentini et al., Tribology in Industry Vol. 40, No. 2 (2018) 165-182 The first scientist who explained a principle that endows fluid bearings with their load carrying capacity was Beauchamp Tower (1845-1904) in 1883-1884.